MATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al. by hand.
|
|
- Laurence Norman
- 5 years ago
- Views:
Transcription
1 MATH 1 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al Mark the point determined by 6 on the unit circle Sketch a graph of y sin( x) by hand Find the amplitude, period, and horizontal shift of the graph of ycos3x , 5.. Graph each function by hand: a. y cos(3x) b. ysin3x c. ytan x Write the equation of the graph in the form y asin k( x b). y x Evaluate sin , Evaluate exactly. a. sin 1 sin. 1 b. cossin Find one positive and one negative angle coterminal with: a. 37 b Convert 3 a. radians to degree measure. b. 196 to radian measure. Round to the nearest hundredth The roller on a treadmill has a diameter of 3 inches. How many revolutions per minute must it make in order for Josh to run at a speed of 10 miles per hour? (1 mile = 5,80 ft)
2 If c represents the length of the hypotenuse, solve the right triangle with a 6 and B If sec and is an acute angle, find sin exactly 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 5 feet away from you to be 70. You also estimate that the gorge is 50 feet wide and want to allow an extra 6 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 six 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 16. After walking inland 00 feet in a direct line with the first observation point, the angle of elevation is about 10. Find the height of the lighthouse if the ground is level Write cot in terms of sin given that is in Quadrant II. 6., Simplify so that the answer contains no trig functions. 1 b 1 a 1 a. tan cos b. sin tan cos Solve the triangle in which a. a, B 7, C 10 b. a 10, B 7, b A pilot is about to land on the 8500 foot runway in Los Angeles. The angles of depression from the plane to the ends of the runway are 16 and 17.. Find the distance the plane must fly before it touches down Solve the triangle in which a 0, b 7, c 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 30 miles from the station, a second is 7 miles, and the angle between the two distances is 37, find how far apart the planes are Simplify cos. 1 sin 7.1. Verify the trig identity: sec x tan x 1 tan x Write an equivalent expression using only one trig function; evaluate exactly. sin(61 )cos(7 ) cos(61 )sin(7 )
3 7.. Find cos(105 ) exactly. (Hint: use an addition or subtraction formula) Given that sin A ; A and tan B ; B, find cos( A B) 5 3 exactly If cos ;, find a. sin( ) b. cos Algebraically find all exact solutions in radians. a. 3sec 0 b Find all real solutions. sin sin 1 c. cos x x 0. sin cos Convert the point 3, from polar to rectangular coordinates Convert the point (, ) from rectangular to polar coordinates a. Graph the point 3, in a polar coordinate system. 6 5 b. State polar coordinates for the point 3, using a positive value of r Convert r 6sin to a rectangular equation Convert x ( y 5) 5 to a polar equation Graph r 5sin(3 ) a. Graph the curve x cos t, y sin t, 0 t. b. Find a rectangular-coordinate equation by eliminating the parameter A ball is thrown with an initial speed of 9 feet per second from a height of 7 feet at an angle of 50 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 x v cos t, y h v sint 16t Given u = 1,, v =, 3, find u 3v Find the direction of the vector 3, The speed of an airplane is 00 mi/hr relative to the air. The wind is blowing due west with a speed of 35 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 3, and 7, 1.
4 9. 1. A horse pulls a wagon horizontally by exerting 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 300 feet Solve the system. x 3y 3 3x y A chemist needs 100 ml of a 7% solution of sulfuric acid, but only has 10% and 0% solutions available. Find how much of each should be used Michigan State University and the University of Michigan scored a total of 50 points during their 015 football game. There were 1 scoring plays: touchdowns, extra point kicks, and field goals at 6, 1, and 3 points respectively. There were twice as many touchdowns as field goals. Find the number of each scoring play for the game Solve each system. If the system is dependent, state the complete solution. a. x y 3z 1 5x y z 5 3x 3y z 1 b. 3x y z x y z 1 7x y 5 c. 3x y z x y z 1 7x y A parabolic reflector for a telescope is six inches in diameter. It is ground so that its vertex is 0.15 inch below the rim (on the concave side). a. Insert an xy coordinate system with vertex at the origin and find the equation of the parabola. b. How far is the focus from the vertex? Find the vertices, foci, and eccentricity of the ellipse with equation x 9y Write the equation of an ellipse centered at the origin containing the point (,0) and with one focus at (0,3) Find the vertex, focus, and directrix of the parabola x 6x y 1 0. Draw the graph Find the center, vertices, foci, and asymptotes of 5x y 00x 8y Draw the graph List the first four terms and the 100 th n term of the sequence an. n Find a formula for the nth term of the sequence 1,,,,, a. Find the fourth partial sum of the sequence 3,1, 7,8,75, b. Evaluate the sum 3k. k 1
5 Write sigma notation for the series Find the first five terms of the sequence where a1 3, an 1 an 1 for n Find the st 31 term of the sequence 8, 5,,1,, Find a 3 a for the arithmetic sequence which has a 7 7 and a Evaluate the sum 3 k 1 k Each row in an auditorium seats more people that the preceding row. There are 5 seats in the first row and 8 rows. Find the seating capacity of the auditorium Find the 10th term of the geometric sequence 81 1,18,7,, Find a formula for the nth (general) term of the sequence, 1, 6, 3, Find the sum. 1 k 1 k Determine whether the infinite geometric series divergent. If it is convergent, find its sum. k 1 8 is convergent or k You have a job offer with a salary of $50,000 for the first year. If you accept the job and get a.5% raise every year for the next 30 years, what are your total earnings for the entire 30 years? Expand and simplify: a. b. 1 x 5 x 3) using the binomial theorem ( using Pascal s triangle. x Find the tenth term in the binomial expansion of x The probability that a softball player hitting.50 will get a hit 3 times in the next eight at bats is the term in which.5 has an exponent of 3 in the binomial expansion of 8 ( ). Find that probability. 17
MATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al
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,
More informationMath 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 informationMULTIPLE 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 informationsin30 = 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 informationPART 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 informationPart 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 informationMATH 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 informationYoungstown 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 information1) 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 informationPLANE 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 informationPre-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 informationPlane 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 informationMULTIPLE 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 informationMultiple 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 informationMath 2412 Activity 4(Due with Final Exam)
Math Activity (Due with Final Exam) Use properties of similar triangles to find the values of x and y x y 7 7 x 5 x y 7 For the angle in standard position with the point 5, on its terminal side, find the
More informationTrigonometry 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 informationSemester 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 informationSHORT 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 informationMA 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 informationTrigonometric 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 informationName: 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 informationMath 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 informationx 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 informationRELEASED. 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 informationUnit 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 informationCh 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 informationHonors 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 informationPrecalculus. 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 information5.1 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 informationMATH 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 informationPart 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 informationAlgebra 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 information3. 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 informationYou 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: 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 informationInverses 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 informationPART 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 informationTrigonometry 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 information4-1 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 informationUnit 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 informationSENIOR 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 informationName: Date: 1. Match the equation with its graph. Page 1
Name: Date: 1. Match the equation with its graph. y 6x A) C) Page 1 D) E) Page . Match the equation with its graph. ( x3) ( y3) A) C) Page 3 D) E) Page 4 3. Match the equation with its graph. ( x ) y 1
More informationReview 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 informationCatholic 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 informationCLEP 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 informationGraphing 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 informationMATH 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 informationPRECALCULUS 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 informationC. 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 informationto and go find the only place where the tangent of that
Study Guide for PART II of the Spring 14 MAT187 Final Exam. NO CALCULATORS are permitted on this part of the Final Exam. This part of the Final exam will consist of 5 multiple choice questions. You will
More informationTrigonometry. 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 information4.8. 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 informationHigh 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 informationSemester 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 information7-5 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 informationPrecalculus 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 informationTriangle 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 informationMATH 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 informationCheckpoint 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, 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 informationPreCalculus 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 informationWeek 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 informationSecondary 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 informationFind 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 informationAlgebra 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 informationTEKS 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 informationAlgebra 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 informationA 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 informationPrecalculus 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 informationMath 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 informationMath 8 EXAM #5 Name: Any work or answers completed on this test form, other than the problems that require you to graph, will not be graded.
Math 8 EXAM #5 Name: Complete all problems in your blue book. Copy the problem into the bluebook then show all of the required work for that problem. Work problems out down the page, not across. Make only
More informationDAY 1 - GEOMETRY FLASHBACK
DAY 1 - GEOMETRY FLASHBACK Sine Opposite Hypotenuse Cosine Adjacent Hypotenuse sin θ = opp. hyp. cos θ = adj. hyp. tan θ = opp. adj. Tangent Opposite Adjacent a 2 + b 2 = c 2 csc θ = hyp. opp. sec θ =
More informationA 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 informationHonors 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 informationReciprocal 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 informationMath 1330 Final Exam Review Covers all material covered in class this semester.
Math 1330 Final Exam Review Covers all material covered in class this semester. 1. Give an equation that could represent each graph. A. Recall: For other types of polynomials: End Behavior An even-degree
More informationContents 10. Graphs of Trigonometric Functions
Contents 10. Graphs of Trigonometric Functions 2 10.2 Sine and Cosine Curves: Horizontal and Vertical Displacement...... 2 Example 10.15............................... 2 10.3 Composite Sine and Cosine
More informationWarm-Up: Final Review #1. A rectangular pen is made from 80 feet of fencing. What is the maximum area the pen can be?
Warm-Up: Final Review #1 A rectangular pen is made from 80 feet of fencing. What is the maximum area the pen can be? Warm-Up: Final Review #2 1) Find distance (-2, 4) (6, -3) 2) Find roots y = x 4-6x 2
More informationuntitled 1. Unless otherwise directed, answers to this question may be left in terms of π.
Name: ate:. Unless otherwise directed, answers to this question may be left in terms of π. a) Express in degrees an angle of π radians. b) Express in radians an angle of 660. c) rod, pivoted at one end,
More informationCatholic Central High School
Catholic Central High School Algebra II Practice Examination I 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 informationName: Period: Final Exam Review
Name: Period: Final Exam Review Note: These problems are NECESSARY but not SUFFICIENT to prepare for the final exam. Be sure to look over your notes, quizzes, and textbook problems as well. Try to summarize
More informationAdvanced Math Final Exam Review Name: Bornoty May June Use the following schedule to complete the final exam review.
Advanced Math Final Exam Review Name: Bornoty May June 2013 Use the following schedule to complete the final exam review. Homework will e checked in every day. Late work will NOT e accepted. Homework answers
More informationChapter 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 informationSection 7.1. Standard position- the vertex of the ray is at the origin and the initial side lies along the positive x-axis.
1 Section 7.1 I. Definitions Angle Formed by rotating a ray about its endpoint. Initial side Starting point of the ray. Terminal side- Position of the ray after rotation. Vertex of the angle- endpoint
More information[B] hours b, P.I. A2.N.9 When simplified,
Math B Regents Exam 0804 Page 1 1. 080401b, P.I. G.G.8 Which condition does not prove that two triangles are congruent? [A] SAS SAS [B] SSA SSA [C] ASA ASA [D] SSS SSS. 08040b, P.I. A.A.5 The speed of
More informationPrecalculus 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 information4.1: 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 informationMastery. 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 informationCK-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 informationFind 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 informationADVANCED ALGEBRA/PRECALCULUS CURRICULUM GUIDE
ADVANCED ALGEBRA/PRECALCULUS CURRICULUM GUIDE Loudoun County Public Schools 2010-2011 Complete scope, sequence, pacing and resources are available on the CD and will be available on the LCPS Intranet.
More informationPractice Test - Chapter 7
Write an equation for an ellipse with each set of characteristics. 1. vertices (7, 4), ( 3, 4); foci (6, 4), ( 2, 4) The distance between the vertices is 2a. 2a = 7 ( 3) a = 5; a 2 = 25 The distance between
More informationAssignment Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Assignment.1-.3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The arch beneath a bridge is semi-elliptical, a one-way
More informationCollege Pre Calculus A Period. Weekly Review Sheet # 1 Assigned: Monday, 9/9/2013 Due: Friday, 9/13/2013
College Pre Calculus A Name Period Weekly Review Sheet # 1 Assigned: Monday, 9/9/013 Due: Friday, 9/13/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE
More informationTo 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 information4. Describe the correlation shown by the scatter plot. 8. Find the distance between the lines with the equations and.
Integrated Math III Summer Review Packet DUE THE FIRST DAY OF SCHOOL The problems in this packet are designed to help you review topics from previous mathematics courses that are essential to your success
More informationMATH EXAM 1 - SPRING 2018 SOLUTION
MATH 140 - EXAM 1 - SPRING 018 SOLUTION 8 February 018 Instructor: Tom Cuchta Instructions: Show all work, clearly and in order, if you want to get full credit. If you claim something is true you must
More informationUnit 3 Trigonometry. 3.4 Graph and analyze the trigonometric functions sine, cosine, and tangent to solve problems.
1 General Outcome: Develop trigonometric reasoning. Specific Outcomes: Unit 3 Trigonometry 3.1 Demonstrate an understanding of angles in standard position, expressed in degrees and radians. 3. Develop
More informationChapter 4: Trigonometry
Chapter 4: Trigonometry Section 4-1: Radian and Degree Measure INTRODUCTION An angle is determined by rotating a ray about its endpoint. The starting position of the ray is the of the angle, and the position
More informationDay 4 Trig Applications HOMEWORK
Day 4 Trig Applications HOMEWORK 1. In ΔABC, a = 0, b = 1, and mc = 44º a) Find the length of side c to the nearest integer. b) Find the area of ΔABC to the nearest tenth.. In ΔABC, ma = 50º, a = 40, b
More information