MATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al

Size: px
Start display at page:

Download "MATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al"

Transcription

1 MATH Final Eam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al.. Mark the point determined by on the unit circle... Sketch a graph of y = sin( ) by hand... Find the amplitude, period, and horizontal shift of the graph of y= cos +..,.. Graph each function by hand: a. y = cos() b. y= sin c. y= tan +.. Write the equation of the graph in the form y asin ( k( b) ) =. y Evaluate sin..,. 7. Evaluate eactly. a. sin sin. b. cos sin.. 8. Find one positive and one negative angle coterminal with: a. 7 b a. Convert radians to degree measure. b. Convert 9 to radian measure. Round to the nearest hundredth.. 0. The roller on a treadmill has a diameter of inches. How many revolutions per minute must it make in order for Josh to run at a speed of 0 miles per hour? ( mile =,80 ft)

2 .. If c represents the length of the hypotenuse, solve the right triangle with a = and B = If sec = and is an acute angle, find sin eactly... You are a tour guide lost in the Rockies and have just come to a gorge. You estimate the angle of elevation of the top of the useful part of a tree that is feet away from you to be 70. You also estimate that the gorge is 0 feet wide and want to allow an etra feet on each end for safety. Will the useable part of the tree be long enough to bridge the gorge if you cut the tree? (Note: the tree just happens to be standing si feet from the edge of the gorge.).. You are estimating the height of a lighthouse surrounded by water. When you first observe it from the shoreline, the angle of elevation seems to be about. After walking inland 00 feet in a direct line with the first observation point, the angle of elevation is about 0. Find the height of the lighthouse if the ground is level... Write cot in terms of sin given that is in Quadrant II.., 7.. Simplify so that the answer contains no trig functions. b a a. tan cos b. sin tan + cos Solve the triangle in which a. a=, B= 7, C = 0 b. a = 0, B = 7, b =. 8. A pilot is about to land on the 800 foot runway in Los Angeles. The angles of depression from the plane to the ends of the runway are and 7.. Find the distance the plane must fly before it touches down.. 9. Solve the triangle in which a = 0, b = 7, c =.. 0. The distance between two planes is calculated by using LORAN to find the position of each plane relative to the tracking station. If one plane is 0 miles from the station, a second is 7 miles, and the angle between the two distances is 7, find how far apart the planes are. cos 7.. Simplify. + sin 7.. Verify the trig identity: sec tan = + tan. 7.. Write an equivalent epression using only one trig function; evaluate eactly. sin( )cos(7 ) + cos( )sin(7 )

3 7.. Find cos( 0 ) eactly. (Hint: use an addition or subtraction formula) 7.. Given that sin A= ; < A < and tan B= ; < B <, find cos( A B) eactly. 7.. If cos = ; < <, find a. sin( ) b. cos Algebraically find all eact solutions in radians. a. sec + = 0 b Find all real solutions. sin sin = c. cos = 0. sin + cos = Convert the point, from polar to rectangular coordinates Convert the point (, ) from rectangular to polar coordinates. 8.. a. Graph the point, in a polar coordinate system. b. State polar coordinates for the point, using a positive value of r. 8.. Convert r = sin to a rectangular equation. 8.. Convert + ( y ) = to a polar equation. 8.. Graph r = sin( ). 8.. a. Graph the curve = cos t, y = sin t, 0 t. b. Find a rectangular-coordinate equation by eliminating the parameter. 8.. A ball is thrown with an initial speed of 9 feet per second from a height of 7 feet at an angle of 0 to the horizontal. You may assume that the ground is level. a. Find the height of the ball after seconds. b. Determine the horizontal distance the ball travels. Use the parametric equations = ( v cos ) t, y = h + ( v sin ) t t Given u =,, v =,, find u v Find the direction of the vector, The speed of an airplane is 00 mi/hr relative to the air. The wind is blowing due west with a speed of mi/hr. In what direction should the airplane head in order to arrive at a point due south of its location? Find the angle between, and 7,.

4 9.. A horse pulls a wagon horizontally by eerting a force of 0 pounds on the handle. If the handle makes an angle of 0 with the horizontal, find the work done in moving the wagon 00 feet. + y = 0.. Solve the system. + y = 0.. A chemist needs 00 ml of a 7% solution of sulfuric acid, but only has 0% and 0% solutions available. Find how much of each should be used. 0.. Michigan State University and the University of Michigan scored a total of 0 points during their 0 football game. There were scoring plays: touchdowns, etra point kicks, and field goals at,, and points respectively. There were twice as many touchdowns as field goals. Find the number of each scoring play for the game. 0.. Solve each system. If the system is dependent, state the complete solution. a. + y + z = + y + z = + y + z = b. + y z = y + z = 7 + y = c. + y z = y + z = 7 + y =.. A parabolic reflector for a telescope is si inches in diameter. It is ground so that its verte is 0. inch below the rim (on the concave side). a. Insert an y coordinate system with verte at the origin and find the equation of the parabola. b. How far is the focus from the verte?. 7. Find the vertices, foci, and eccentricity of the ellipse with equation + 9y =.. 8. Write the equation of an ellipse centered at the origin containing the point (,0) and with one focus at (0,).. 9. Find the verte, focus, and directri of the parabola + + y + = 0. Draw the graph.. 0. Find the center, vertices, foci, and asymptotes of y y + 9 = 0. Draw the graph... List the first four terms and the 00 th n term of the sequence an =. n +.. Find a formula for the nth term of the sequence,,,,, a. Find the fourth partial sum of the sequence,, 7,8,7, b. Evaluate the sum k. k =

5 .. Write sigma notation for the series Find the first five terms of the sequence where a =, an+ = an + for n... Find the st term of the sequence 8,,,,, Find a a for the arithmetic sequence which has a 7 = 7 and a 0 = Evaluate the sum k = k Each row in an auditorium seats more people that the preceding row. There are seats in the first row and 8 rows. Find the seating capacity of the auditorium.. 0. Find the 0th term of the geometric sequence 8,8,7,,..... Find a formula for the nth (general) term of the sequence,,,,.. Find the sum. k = k 8.. Determine whether the infinite geometric series divergent. If it is convergent, find its sum. k = k 8 is convergent or.. You have a job offer with a salary of $0,000 for the first year. If you accept the job and get a.% raise every year for the net 0 years, what are your total earnings for the entire 0 years?.. Epand and simplify: a. ( ) using the binomial theorem b. using Pascal s triangle. +.. Find the tenth term in the binomial epansion of. 7. The probability that a softball player hitting.0 will get a hit times in the net eight at bats is the term in which. has an eponent of in the binomial epansion of 8 ( ). Find that probability. 7.

MATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al. by hand.

MATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al. by hand. MATH 1 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al 5.1 1. Mark the point determined by 6 on the unit circle. 5.3. Sketch a graph of y sin( x) by hand. 5.3 3. Find the

More information

Pre-Calculus Right Triangle Trigonometry Review Name Dec π

Pre-Calculus Right Triangle Trigonometry Review Name Dec π Pre-Calculus Right Triangle Trigonometry Review Name Dec 201 Convert from Radians to Degrees, or Degrees to Radians 7π 1. 0 2.. 1. 11π. Find the si trig functions of θ. If sin θ =, find the other five

More information

Math 370 Exam 5 Review Name

Math 370 Exam 5 Review Name Math 370 Exam 5 Review Name Graph the ellipse and locate the foci. 1) x2 6 + y2 = 1 1) Objective: (9.1) Graph Ellipses Not Centered at the Origin Graph the ellipse. 2) (x + 2)2 + (y + 1)2 9 = 1 2) Objective:

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 1)

More information

sin30 = sin60 = cos30 = cos60 = tan30 = tan60 =

sin30 = sin60 = cos30 = cos60 = tan30 = tan60 = Precalculus Notes Trig-Day 1 x Right Triangle 5 How do we find the hypotenuse? 1 sinθ = cosθ = tanθ = Reciprocals: Hint: Every function pair has a co in it. sinθ = cscθ = sinθ = cscθ = cosθ = secθ = cosθ

More information

Precalculus. Cumulative Review Conics, Polar, Parametric, Sequences & Series, Rational Functions. Conics

Precalculus. Cumulative Review Conics, Polar, Parametric, Sequences & Series, Rational Functions. Conics Name Precalculus Date Block Cumulative Review Conics, Polar, Parametric, Sequences & Series, Rational Functions Please do all work on a separate sheet of paper Conics Identify each equation If it is a

More information

PART I You must complete this portion of the test without using a calculator. After you

PART I You must complete this portion of the test without using a calculator. After you Salt Lake Community College Math 1060 Final Exam A Fall Semester 2010 Name: Instructor: This Exam has three parts. Please read carefully the directions for each part. All problems are of equal point value.

More information

1) The domain of y = sin-1x is The range of y = sin-1x is. 2) The domain of y = cos-1x is The range of y = cos-1x is

1) The domain of y = sin-1x is The range of y = sin-1x is. 2) The domain of y = cos-1x is The range of y = cos-1x is MAT 204 NAME TEST 4 REVIEW ASSIGNMENT Sections 8.1, 8.3-8.5, 9.2-9.3, 10.1 For # 1-3, fill in the blank with the appropriate interval. 1) The domain of y = sin-1x is The range of y = sin-1x is 2) The domain

More information

MATH 1112 Trigonometry Final Exam Review

MATH 1112 Trigonometry Final Exam Review MATH 1112 Trigonometry Final Exam Review 1. Convert 105 to exact radian measure. 2. Convert 2 to radian measure to the nearest hundredth of a radian. 3. Find the length of the arc that subtends an central

More information

Youngstown State University Trigonometry Final Exam Review (Math 1511)

Youngstown State University Trigonometry Final Exam Review (Math 1511) Youngstown State University Trigonometry Final Exam Review (Math 1511) 1. Convert each angle measure to decimal degree form. (Round your answers to thousandths place). a) 75 54 30" b) 145 18". Convert

More information

Precalculus CP Final Exam Review. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Precalculus CP Final Exam Review. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Precalculus CP Final Eam Review Name Date: / / MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Epress answer

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Review for Test 2 MATH 116 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the right triangle. If two sides are given, give angles in degrees and

More information

Multiple Choice Questions Circle the letter of the correct answer. 7 points each. is:

Multiple Choice Questions Circle the letter of the correct answer. 7 points each. is: This Math 114 final exam was administered in the Fall of 008. This is a sample final exam. The problems are not exhaustive. Be prepared for ALL CONCEPTS for the actual final exam. Multiple Choice Questions

More information

Trigonometry Review Day 1

Trigonometry Review Day 1 Name Trigonometry Review Day 1 Algebra II Rotations and Angle Terminology II Terminal y I Positive angles rotate in a counterclockwise direction. Reference Ray Negative angles rotate in a clockwise direction.

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Precalculus CP Final Exam Review - 01 Name Date: / / MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Express

More information

Plane Trigonometry Test File Fall 2014

Plane Trigonometry Test File Fall 2014 Plane Trigonometry Test File Fall 2014 Test #1 1.) Fill in the blanks in the two tables with the EXACT values (no calculator) of the given trigonometric functions. The total point value for the tables

More information

Name: Block: What I can do for this unit:

Name: Block: What I can do for this unit: Unit 8: Trigonometry Student Tracking Sheet Math 10 Common Name: Block: What I can do for this unit: After Practice After Review How I Did 8-1 I can use and understand triangle similarity and the Pythagorean

More information

PLANE TRIGONOMETRY Exam I September 13, 2007

PLANE TRIGONOMETRY Exam I September 13, 2007 Name Rec. Instr. Rec. Time PLANE TRIGONOMETRY Exam I September 13, 2007 Page 1 Page 2 Page 3 Page 4 TOTAL (10 pts.) (30 pts.) (30 pts.) (30 pts.) (100 pts.) Below you will find 10 problems, each worth

More information

Part I. There are 5 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer.

Part I. There are 5 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer. Math 109 Final Exam-Spring 016 Page 1 Part I. There are 5 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer. 1) Determine an equivalent

More information

Honors Pre-Calculus. 6.1: Vector Word Problems

Honors Pre-Calculus. 6.1: Vector Word Problems Honors Pre-Calculus 6.1: Vector Word Problems 1. A sled on an inclined plane weighs 00 lb, and the plane makes an angle of 0 degrees with the horizontal. What force, perpendicular to the plane, is exerted

More information

Trigonometric Ratios and Functions

Trigonometric Ratios and Functions Algebra 2/Trig Unit 8 Notes Packet Name: Date: Period: # Trigonometric Ratios and Functions (1) Worksheet (Pythagorean Theorem and Special Right Triangles) (2) Worksheet (Special Right Triangles) (3) Page

More information

ALGEBRA 2 CP FINAL EXAM REVIEW

ALGEBRA 2 CP FINAL EXAM REVIEW ALGEBRA CP FINAL EXAM REVIEW Algebra CP FINAL EXAM REVIEW Name CHAPTER - TRIGONOMETRY Note: always round sides to the nearest tenth and angles to the nearest degree. Find the values of the si trigonometric

More information

MA 154 PRACTICE QUESTIONS FOR THE FINAL 11/ The angles with measures listed are all coterminal except: 5π B. A. 4

MA 154 PRACTICE QUESTIONS FOR THE FINAL 11/ The angles with measures listed are all coterminal except: 5π B. A. 4 . If θ is in the second quadrant and sinθ =.6, find cosθ..7.... The angles with measures listed are all coterminal except: E. 6. The radian measure of an angle of is: 7. Use a calculator to find the sec

More information

Ch 7 & 8 Exam Review. Note: This is only a sample. Anything covered in class or homework may appear on the exam.

Ch 7 & 8 Exam Review. Note: This is only a sample. Anything covered in class or homework may appear on the exam. Ch 7 & 8 Exam Review Note: This is only a sample. Anything covered in class or homework may appear on the exam. Determine whether there is sufficient information for solving a triangle, with the given

More information

Inverses of Trigonometric. Who uses this? Hikers can use inverse trigonometric functions to navigate in the wilderness. (See Example 3.

Inverses of Trigonometric. Who uses this? Hikers can use inverse trigonometric functions to navigate in the wilderness. (See Example 3. 1-4 Inverses of Trigonometric Functions Objectives Evaluate inverse trigonometric functions. Use trigonometric equations and inverse trigonometric functions to solve problems. Vocabulary inverse sine function

More information

7-5 Parametric Equations

7-5 Parametric Equations 3. Sketch the curve given by each pair of parametric equations over the given interval. Make a table of values for 6 t 6. t x y 6 19 28 5 16.5 17 4 14 8 3 11.5 1 2 9 4 1 6.5 7 0 4 8 1 1.5 7 2 1 4 3 3.5

More information

Precalculus 2 Section 10.6 Parametric Equations

Precalculus 2 Section 10.6 Parametric Equations Precalculus 2 Section 10.6 Parametric Equations Parametric Equations Write parametric equations. Graph parametric equations. Determine an equivalent rectangular equation for parametric equations. Determine

More information

Triangle Trigonometry

Triangle Trigonometry Honors Finite/Brief: Trigonometry review notes packet Triangle Trigonometry Right Triangles All triangles (including non-right triangles) Law of Sines: a b c sin A sin B sin C Law of Cosines: a b c bccos

More information

Trigonometry Final Review Exercises

Trigonometry Final Review Exercises 1 The exam will last 2 hours and will be entirely short answer. Be sure to provide adequate written work to justify your answers in order to receive full credit. You will be provided with a basic trig

More information

Algebra 2 Semester 2 Midterm Review

Algebra 2 Semester 2 Midterm Review Algebra Semester Midterm Review NON-CALCULATOR 5.7 1. Using the graph of f ( ) or f ( ) as a guide, describe the transformation, fill in the table, and graph each function. Then, identif the domain and

More information

Semester 2 Review Units 4, 5, and 6

Semester 2 Review Units 4, 5, and 6 Precalculus Semester 2 Review Units 4, 5, and 6 NAME: Period: UNIT 4 Simplify each expression. 1) (sec θ tan θ)(1 + tan θ) 2) cos θ sin 2 θ 1 3) 1+tan θ 1+cot θ 4) cos 2θ cosθ sin θ 5) sec 2 x sec 2 x

More information

4-1 Right Triangle Trigonometry

4-1 Right Triangle Trigonometry Find the exact values of the six trigonometric functions of θ. 1. sin θ =, cos θ =, tan θ =, csc θ 5. sin θ =, cos θ =, tan θ =, csc θ =, sec θ =, cot θ = =, sec θ =, cot θ = 2. sin θ =, cos θ =, tan θ

More information

Week 8 Problems. #2 Points possible: 1. Total attempts: 2 Enter your answer rounded to two decimal places.

Week 8 Problems. #2 Points possible: 1. Total attempts: 2 Enter your answer rounded to two decimal places. Week 8 Problems Name: Neal Nelson Show Scored View # Points possible:. Total attempts: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts,.6 mi apart, to

More information

Math Analysis Final Exam Review. Chapter 1 Standards

Math Analysis Final Exam Review. Chapter 1 Standards Math Analysis Final Exam Review Chapter 1 Standards 1a 1b 1c 1d 1e 1f 1g Use the Pythagorean Theorem to find missing sides in a right triangle Use the sine, cosine, and tangent functions to find missing

More information

These are the type of problems that you will be working on in class. These problems are from Lesson 7.

These are the type of problems that you will be working on in class. These problems are from Lesson 7. Pre-Class Problems 10 for Wednesda, October 10 These are the tpe of problems that ou will be working on in class. These problems are from Lesson 7. Solution to Problems on the Pre-Eam. You can go to the

More information

Convert the angle to radians. Leave as a multiple of π. 1) 36 1) 2) 510 2) 4) )

Convert the angle to radians. Leave as a multiple of π. 1) 36 1) 2) 510 2) 4) ) MAC Review for Eam Name Convert the angle to radians. Leave as a multiple of. ) 6 ) ) 50 ) Convert the degree measure to radians, correct to four decimal places. Use.6 for. ) 0 9 ) ) 0.0 ) Convert the

More information

C. HECKMAN TEST 2A SOLUTIONS 170

C. HECKMAN TEST 2A SOLUTIONS 170 C HECKMN TEST SOLUTIONS 170 (1) [15 points] The angle θ is in Quadrant IV and tan θ = Find the exact values of 5 sin θ, cos θ, tan θ, cot θ, sec θ, and csc θ Solution: point that the terminal side of the

More information

RELEASED. Student Booklet. Precalculus. Fall 2015 NC Final Exam. Released Items

RELEASED. Student Booklet. Precalculus. Fall 2015 NC Final Exam. Released Items Released Items Public Schools of North arolina State oard of Education epartment of Public Instruction Raleigh, North arolina 27699-6314 Fall 2015 N Final Exam Precalculus Student ooklet opyright 2015

More information

Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them.

Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Chapter 9 and 10: Right Triangles and Trigonometric Ratios 1. The hypotenuse of a right

More information

Math Released Item Geometry. Height of Support VF650053

Math Released Item Geometry. Height of Support VF650053 Math Released Item 2016 Geometry Height of Support VF650053 Prompt Task is worth a total of 3 points. Rubric VF650053 Rubric Part A Score Description 2 Student response includes the following 2 elements.

More information

Unit 7: Trigonometry Part 1

Unit 7: Trigonometry Part 1 100 Unit 7: Trigonometry Part 1 Right Triangle Trigonometry Hypotenuse a) Sine sin( α ) = d) Cosecant csc( α ) = α Adjacent Opposite b) Cosine cos( α ) = e) Secant sec( α ) = c) Tangent f) Cotangent tan(

More information

MATH 229 TRIGONOMETRY. COURSE PACK (Fall 2018) Mark Turner Mathematics Division Cuesta College

MATH 229 TRIGONOMETRY. COURSE PACK (Fall 2018) Mark Turner Mathematics Division Cuesta College MATH 9 TRIGONOMETRY COURSE PACK (Fall 08) Mark Turner Mathematics Division Cuesta College Angles and Triangles. Find the complement and supplement of 60. Complement = Supplement =. Use the Pythagorean

More information

5.1 Angles & Their Measures. Measurement of angle is amount of rotation from initial side to terminal side. radians = 60 degrees

5.1 Angles & Their Measures. Measurement of angle is amount of rotation from initial side to terminal side. radians = 60 degrees .1 Angles & Their Measures An angle is determined by rotating array at its endpoint. Starting side is initial ending side is terminal Endpoint of ray is the vertex of angle. Origin = vertex Standard Position:

More information

MATH 1040 CP 15 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MATH 1040 CP 15 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. MATH 1040 CP 15 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the triangle. 1) 1) 80 7 55 Solve the triangle. Round lengths to the nearest tenth

More information

CLEP Pre-Calculus. Section 1: Time 30 Minutes 50 Questions. 1. According to the tables for f(x) and g(x) below, what is the value of [f + g]( 1)?

CLEP Pre-Calculus. Section 1: Time 30 Minutes 50 Questions. 1. According to the tables for f(x) and g(x) below, what is the value of [f + g]( 1)? CLEP Pre-Calculus Section : Time 0 Minutes 50 Questions For each question below, choose the best answer from the choices given. An online graphing calculator (non-cas) is allowed to be used for this section..

More information

sin 2 2sin cos The formulas below are provided in the examination booklet. Trigonometric Identities: cos sin cos sin sin cos cos sin

sin 2 2sin cos The formulas below are provided in the examination booklet. Trigonometric Identities: cos sin cos sin sin cos cos sin The semester A eamination for Precalculus consists of two parts. Part 1 is selected response on which a calculator will not be allowed. Part is short answer on which a calculator will be allowed. Pages

More information

MATH 1113 Practice Test 5 SPRING 2016

MATH 1113 Practice Test 5 SPRING 2016 MATH 1113 Practice Test 5 SPRING 016 1. Solve the right triangle given that 37 and b = 4. (find all the missing parts) Find the area. Solve the right triangle given that 16 and a = 31. (find all the missing

More information

x y 2 2 CONIC SECTIONS Problem 1

x y 2 2 CONIC SECTIONS Problem 1 CONIC SECTIONS Problem For the equations below, identify each conic section If it s a parabola, specify its vertex, focus and directrix If it s an ellipse, specify its center, vertices and foci If it s

More information

CK-12 Geometry: Inverse Trigonometric Ratios

CK-12 Geometry: Inverse Trigonometric Ratios CK-12 Geometry: Inverse Trigonometric Ratios Learning Objectives Use the inverse trigonometric ratios to find an angle in a right triangle. Solve a right triangle. Apply inverse trigonometric ratios to

More information

Checkpoint 1 Define Trig Functions Solve each right triangle by finding all missing sides and angles, round to four decimal places

Checkpoint 1 Define Trig Functions Solve each right triangle by finding all missing sides and angles, round to four decimal places Checkpoint 1 Define Trig Functions Solve each right triangle by finding all missing sides and angles, round to four decimal places. 1.. B P 10 8 Q R A C. Find the measure of A and the length of side a..

More information

Algebra II. Chapter 13 Notes Sections 13.1 & 13.2

Algebra II. Chapter 13 Notes Sections 13.1 & 13.2 Algebra II Chapter 13 Notes Sections 13.1 & 13.2 Name Algebra II 13.1 Right Triangle Trigonometry Day One Today I am using SOHCAHTOA and special right triangle to solve trig problems. I am successful

More information

Algebra II Trigonometric Functions

Algebra II Trigonometric Functions Slide 1 / 162 Slide 2 / 162 Algebra II Trigonometric Functions 2015-12-17 www.njctl.org Slide 3 / 162 Trig Functions click on the topic to go to that section Radians & Degrees & Co-terminal angles Arc

More information

Ready To Go On? Skills Intervention 8-1 Similarity in Right Triangles

Ready To Go On? Skills Intervention 8-1 Similarity in Right Triangles 8 Find this vocabular word in Lesson 8-1 and the Multilingual Glossar. Finding Geometric Means The geometric mean of two positive numbers is the positive square root of their. Find the geometric mean of

More information

AW Math 10 UNIT 7 RIGHT ANGLE TRIANGLES

AW Math 10 UNIT 7 RIGHT ANGLE TRIANGLES AW Math 10 UNIT 7 RIGHT ANGLE TRIANGLES Assignment Title Work to complete Complete 1 Triangles Labelling Triangles 2 Pythagorean Theorem 3 More Pythagorean Theorem Eploring Pythagorean Theorem Using Pythagorean

More information

Algebra II. Slide 1 / 162. Slide 2 / 162. Slide 3 / 162. Trigonometric Functions. Trig Functions

Algebra II. Slide 1 / 162. Slide 2 / 162. Slide 3 / 162. Trigonometric Functions. Trig Functions Slide 1 / 162 Algebra II Slide 2 / 162 Trigonometric Functions 2015-12-17 www.njctl.org Trig Functions click on the topic to go to that section Slide 3 / 162 Radians & Degrees & Co-terminal angles Arc

More information

PRECALCULUS MATH Trigonometry 9-12

PRECALCULUS MATH Trigonometry 9-12 1. Find angle measurements in degrees and radians based on the unit circle. 1. Students understand the notion of angle and how to measure it, both in degrees and radians. They can convert between degrees

More information

Theorem 8-1-1: The three altitudes in a right triangle will create three similar triangles

Theorem 8-1-1: The three altitudes in a right triangle will create three similar triangles G.T. 7: state and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. Understand and use the geometric mean to solve for missing parts of triangles. 8-1

More information

Catholic Central High School

Catholic Central High School Catholic Central High School Algebra II Practice Examination II Instructions: 1. Show all work on the test copy itself for every problem where work is required. Points may be deducted if insufficient or

More information

A lg e b ra II. Trig o n o m e tric F u n c tio

A lg e b ra II. Trig o n o m e tric F u n c tio 1 A lg e b ra II Trig o n o m e tric F u n c tio 2015-12-17 www.njctl.org 2 Trig Functions click on the topic to go to that section Radians & Degrees & Co-terminal angles Arc Length & Area of a Sector

More information

A trigonometric ratio is a,

A trigonometric ratio is a, ALGEBRA II Chapter 13 Notes The word trigonometry is derived from the ancient Greek language and means measurement of triangles. Section 13.1 Right-Triangle Trigonometry Objectives: 1. Find the trigonometric

More information

Part I. There are 8 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer.

Part I. There are 8 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer. Math 109 Final Final Exam-Spring 2018 Page 1 Part I. There are 8 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer. 1) Determine an equivalent

More information

Honors Precalculus: Solving equations and inequalities graphically and algebraically. Page 1

Honors Precalculus: Solving equations and inequalities graphically and algebraically. Page 1 Solving equations and inequalities graphically and algebraically 1. Plot points on the Cartesian coordinate plane. P.1 2. Represent data graphically using scatter plots, bar graphs, & line graphs. P.1

More information

You ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of the = 46

You ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of the = 46 Math 1330 Section 6.2 Section 7.1: Right-Triangle Applications In this section, we ll solve right triangles. In some problems you will be asked to find one or two specific pieces of information, but often

More information

Practice For use with pages

Practice For use with pages 9.1 For use with pages 453 457 Find the square roots of the number. 1. 36. 361 3. 79 4. 1089 5. 4900 6. 10,000 Approimate the square root to the nearest integer. 7. 39 8. 85 9. 105 10. 136 11. 17.4 1.

More information

Chapter 7. Right Triangles and Trigonometry

Chapter 7. Right Triangles and Trigonometry hapter 7 Right Triangles and Trigonometry 7.1 pply the Pythagorean Theorem 7.2 Use the onverse of the Pythagorean Theorem 7.3 Use Similar Right Triangles 7.4 Special Right Triangles 7.5 pply the Tangent

More information

Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.

Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary. Name Homework Packet 7.6 7.7 LESSON 7.6 For use with pages 473-480 AND LESSON 7.7 For use with pages 483 489 Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal.

More information

MIDTERM 3 PART 1 (CHAPTER 4) INTRODUCTION TO TRIGONOMETRY; MATH 141 FALL 2018 KUNIYUKI 150 POINTS TOTAL: 30 FOR PART 1, AND 120 FOR PART

MIDTERM 3 PART 1 (CHAPTER 4) INTRODUCTION TO TRIGONOMETRY; MATH 141 FALL 2018 KUNIYUKI 150 POINTS TOTAL: 30 FOR PART 1, AND 120 FOR PART Math 141 Name: MIDTERM PART 1 (CHAPTER 4) INTRODUCTION TO TRIGONOMETRY; MATH 141 FALL 2018 KUNIYUKI 150 POINTS TOTAL: 0 FOR PART 1, AND 120 FOR PART 2 Show all work, simplify as appropriate, and use good

More information

High School MATHEMATICS Trigonometry

High School MATHEMATICS Trigonometry High School MATHEMATICS Trigonometry Curriculum Curriculum Map USD 457 Math Framework Performance/Open-Ended Response Assessments o First Semester (Tasks 1-3) o Second Semester (Tasks 1-4) Available on

More information

Unit O Student Success Sheet (SSS) Right Triangle Trigonometry (sections 4.3, 4.8)

Unit O Student Success Sheet (SSS) Right Triangle Trigonometry (sections 4.3, 4.8) Unit O Student Success Sheet (SSS) Right Triangle Trigonometry (sections 4.3, 4.8) Standards: Geom 19.0, Geom 20.0, Trig 7.0, Trig 8.0, Trig 12.0 Segerstrom High School -- Math Analysis Honors Name: Period:

More information

Precalculus 4.1 Notes Angle Measures, Arc Length, and Sector Area

Precalculus 4.1 Notes Angle Measures, Arc Length, and Sector Area Precalculus 4.1 Notes Angle Measures, Arc Length, and Sector Area An angle can be formed by rotating one ray away from a fixed ray indicated by an arrow. The fixed ray is the initial side and the rotated

More information

PART I: NO CALCULATOR (64 points)

PART I: NO CALCULATOR (64 points) Math 10 Trigonometry 11 th edition Lial, Hornsby, Schneider, and Daniels Practice Midterm (Ch. 1-) PART I: NO CALCULATOR (6 points) (.1,.,.,.) Match each graph with one of the basic circular functions

More information

Skills Practice Skills Practice for Lesson 7.1

Skills Practice Skills Practice for Lesson 7.1 Skills Practice Skills Practice for Lesson.1 Name Date Tangent Ratio Tangent Ratio, Cotangent Ratio, and Inverse Tangent Vocabulary Match each description to its corresponding term for triangle EFG. F

More information

3. Solve the following. Round to the nearest thousandth.

3. Solve the following. Round to the nearest thousandth. This review does NOT cover everything! Be sure to go over all notes, homework, and tests that were given throughout the semester. 1. Given g ( x) i, h( x) x 4x x, f ( x) x, evaluate the following: a) f

More information

Trigonometry. Secondary Mathematics 3 Page 180 Jordan School District

Trigonometry. Secondary Mathematics 3 Page 180 Jordan School District Trigonometry Secondary Mathematics Page 80 Jordan School District Unit Cluster (GSRT9): Area of a Triangle Cluster : Apply trigonometry to general triangles Derive the formula for the area of a triangle

More information

Solving Right Triangles. SECURITY A security light is being

Solving Right Triangles. SECURITY A security light is being 5-5 OJECTIVES Evaluate inverse trigonometric functions. Find missing angle measurements. Solve right triangles. Solving Right Triangles SECURITY A security light is being installed outside a loading dock.

More information

Introduction to Trigonometry

Introduction to Trigonometry NAME COMMON CORE GEOMETRY- Unit 6 Introduction to Trigonometry DATE PAGE TOPIC HOMEWORK 1/22 2-4 Lesson 1 : Incredibly Useful Ratios Homework Worksheet 1/23 5-6 LESSON 2: Using Trigonometry to find missing

More information

Graphing Trigonometric Functions: Day 1

Graphing Trigonometric Functions: Day 1 Graphing Trigonometric Functions: Day 1 Pre-Calculus 1. Graph the six parent trigonometric functions.. Apply scale changes to the six parent trigonometric functions. Complete the worksheet Exploration:

More information

Reciprocal Identities Quotient Identities Pythagorean Identities

Reciprocal Identities Quotient Identities Pythagorean Identities 2 Precalculus Review Sheet 4.2 4.4 Fundamental Identities: Reciprocal Identities Quotient Identities Pythagorean Identities = csc! cos! = tan! sin2! + cos 2! = cos! = sec! cos! = cot! tan2! + = sec 2!

More information

: Find the values of the six trigonometric functions for θ. Special Right Triangles:

: Find the values of the six trigonometric functions for θ. Special Right Triangles: ALGEBRA 2 CHAPTER 13 NOTES Section 13-1 Right Triangle Trig Understand and use trigonometric relationships of acute angles in triangles. 12.F.TF.3 CC.9- Determine side lengths of right triangles by using

More information

SENIOR HIGH MATH LEAGUE April 24, GROUP IV Emphasis on TRIGONOMETRY

SENIOR HIGH MATH LEAGUE April 24, GROUP IV Emphasis on TRIGONOMETRY SENIOR HIGH MATH LEAGUE TEST A Write all radical expressions in simplified form and unless otherwise stated give exact answers. 1. Give the exact value for each of the following where the angle is given

More information

4.8. Solving Problems with Trigonometry. Copyright 2011 Pearson, Inc.

4.8. Solving Problems with Trigonometry. Copyright 2011 Pearson, Inc. 4.8 Solving Problems with Trigonometry Copyright 2011 Pearson, Inc. What you ll learn about More Right Triangle Problems Simple Harmonic Motion and why These problems illustrate some of the better- known

More information

Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them.

Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Chapter 9 and 10: Right Triangles and Trigonometric Ratios 1. The hypotenuse of a right

More information

TEKS Clarification Document. Mathematics Precalculus

TEKS Clarification Document. Mathematics Precalculus TEKS Clarification Document Mathematics Precalculus 2012 2013 111.31. Implementation of Texas Essential Knowledge and Skills for Mathematics, Grades 9-12. Source: The provisions of this 111.31 adopted

More information

PreCalculus Chapter 9 Practice Test Name:

PreCalculus Chapter 9 Practice Test Name: This ellipse has foci 0,, and therefore has a vertical major axis. The standard form for an ellipse with a vertical major axis is: 1 Note: graphs of conic sections for problems 1 to 1 were made with the

More information

, minor axis of length 12. , asymptotes y 2x. 16y

, minor axis of length 12. , asymptotes y 2x. 16y Math 4 Midterm 1 Review CONICS [1] Find the equations of the following conics. If the equation corresponds to a circle find its center & radius. If the equation corresponds to a parabola find its focus

More information

Unit 4 Trigonometry. Study Notes 1 Right Triangle Trigonometry (Section 8.1)

Unit 4 Trigonometry. Study Notes 1 Right Triangle Trigonometry (Section 8.1) Unit 4 Trigonometr Stud Notes 1 Right Triangle Trigonometr (Section 8.1) Objective: Evaluate trigonometric functions of acute angles. Use a calculator to evaluate trigonometric functions. Use trigonometric

More information

4.1: Angles & Angle Measure

4.1: Angles & Angle Measure 4.1: Angles & Angle Measure In Trigonometry, we use degrees to measure angles in triangles. However, degree is not user friendly in many situations (just as % is not user friendly unless we change it into

More information

Chapter 3: Right Triangle Trigonometry

Chapter 3: Right Triangle Trigonometry 10C Name: Chapter 3: Right Triangle Trigonometry 3.1 The Tangent Ratio Outcome : Develop and apply the tangent ratio to solve problems that involve right triangles. Definitions: Adjacent side: the side

More information

Trigonometry and the Unit Circle. Chapter 4

Trigonometry and the Unit Circle. Chapter 4 Trigonometry and the Unit Circle Chapter 4 Topics Demonstrate an understanding of angles in standard position, expressed in degrees and radians. Develop and apply the equation of the unit circle. Solve

More information

Precalculus eday #3 Assignment

Precalculus eday #3 Assignment Name Date Score Precalculus eday #3 Assignment 1. If X = 35, Y = 84, and Z = 91, what is the cosine of B? 2. If X = 60, Y = 25, and Z = 65, what is the sine of B? 3. In the triangle shown above m A = 43,

More information

Geo, Chap 8 Practice Test, EV Ver 1

Geo, Chap 8 Practice Test, EV Ver 1 Name: Class: Date: ID: A Geo, Chap 8 Practice Test, EV Ver 1 Short Answer Find the length of the missing side. Leave your answer in simplest radical form. 1. (8-1) 2. (8-1) A grid shows the positions of

More information

Chapter 9 Topics in Analytic Geometry

Chapter 9 Topics in Analytic Geometry Chapter 9 Topics in Analytic Geometry What You ll Learn: 9.1 Introduction to Conics: Parabolas 9.2 Ellipses 9.3 Hyperbolas 9.5 Parametric Equations 9.6 Polar Coordinates 9.7 Graphs of Polar Equations 9.1

More information

To sketch the graph we need to evaluate the parameter t within the given interval to create our x and y values.

To sketch the graph we need to evaluate the parameter t within the given interval to create our x and y values. Module 10 lesson 6 Parametric Equations. When modeling the path of an object, it is useful to use equations called Parametric equations. Instead of using one equation with two variables, we will use two

More information

Secondary Mathematics 3 Table of Contents

Secondary Mathematics 3 Table of Contents Secondary Mathematics Table of Contents Trigonometry Unit Cluster 1: Apply trigonometry to general triangles (G.SRT.9)...4 (G.SRT.10 and G.SRT.11)...7 Unit Cluster : Extending the domain of trigonometric

More information

CCA Integrated Math 3 Module 4 Honors & 3.3, 3.5 Trigonometric Functions Ready, Set, Go!

CCA Integrated Math 3 Module 4 Honors & 3.3, 3.5 Trigonometric Functions Ready, Set, Go! 1 CCA Integrated Math 3 Module 4 Honors & 3.3, 3.5 Trigonometric Functions Ready, Set, Go! Adapted from The Mathematics Vision Project: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet

More information

Find the amplitude, period, and phase shift, and vertical translation of the following: 5. ( ) 6. ( )

Find the amplitude, period, and phase shift, and vertical translation of the following: 5. ( ) 6. ( ) 1. Fill in the blanks in the following table using exact values. Reference Angle sin cos tan 11 6 225 2. Find the exact values of x that satisfy the given condition. a) cos x 1, 0 x 6 b) cos x 0, x 2 3.

More information

Find the component form and magnitude of the vector where P = (-3,4), Q = (-5, 2), R = (-1, 3) and S = (4, 7)

Find the component form and magnitude of the vector where P = (-3,4), Q = (-5, 2), R = (-1, 3) and S = (4, 7) PRE-CALCULUS: by Finney,Demana,Watts and Kennedy Chapter 6: Applications of Trigonometry 6.1: Vectors in the Plane What you'll Learn About Two Dimensional Vectors/Vector Operations/Unit Vectors Direction

More information

Review Notes for the Calculus I/Precalculus Placement Test

Review Notes for the Calculus I/Precalculus Placement Test Review Notes for the Calculus I/Precalculus Placement Test Part 9 -. Degree and radian angle measures a. Relationship between degrees and radians degree 80 radian radian 80 degree Example Convert each

More information

Mastery. PRECALCULUS Student Learning Targets

Mastery. PRECALCULUS Student Learning Targets PRECALCULUS Student Learning Targets Big Idea: Sequences and Series 1. I can describe a sequence as a function where the domain is the set of natural numbers. Connections (Pictures, Vocabulary, Definitions,

More information

Solve the following system of equations using either substitution or elimination:

Solve the following system of equations using either substitution or elimination: Mathematics 04 Final Eam Review Topic : Solving a system of equations in three variables. 009 Solve the following system of equations using either substitution or elimination: + y + z 0 + y z y + z Select

More information