Warm-Up: Final Review #1. A rectangular pen is made from 80 feet of fencing. What is the maximum area the pen can be?
|
|
- Mervin Phelps
- 5 years ago
- Views:
Transcription
1 Warm-Up: Final Review #1 A rectangular pen is made from 80 feet of fencing. What is the maximum area the pen can be?
2 Warm-Up: Final Review #2 1) Find distance (-2, 4) (6, -3) 2) Find roots y = x 4-6x ) List all the possible rational roots for y = 3x 4 + 2x 3 6x 2 + 4x - 2
3 Warm-Up: Final Review #3 1) Find the distance between and the midpoint of (0, 6) and (-4, 3). 2) Find the equation of the perpendicular bisector of the segment joining points (2, 3) and (5, 9).
4 Warm-Up:Final Review #4 1) Solve log x 27 = 3 2) Expand xy log 6 z 2 4 3) Evaluate log 6 9 in calculator 4) Solve ln e 3x = 45 5) Simplify log log 9 27
5 Warm-Up: Final Review #5 1) f(x) = x 2 + x find f(x - 1) 2) f(x) = 2x, g(x) = 3x 2, find f(g(x))
6 Warm-Up: Final Review #6 1) What kind of symmetry does y 2 = 3x have? 2) Find the vertex of y = (x + 4) x 2 3) Graph f(x) = Give equations of asym. 4) Find the y int of y = x 2-10x + 24
7 Warm-Up: Final Review #7 1) Write an equation through (3, 4) with slope ½ 2) Find the slope of the line 2x 4y = 8 3) Write an equation through (5, -3) and perpendicular to the line 2x 3y = 12 4) Find distance (-2, 4) (6, 3) 5) Find the midpoint (3, 4) (-5, 16) 6) Find the slope (6, 12) (-8, 3)
8 Warm-Up: Final Review #8 1) Simplify i 23 2) Solve 3 3x+7 = 9 x-1 3) Simplify ((x -2 ) -1 ) 0 4) Solve 3 2x = 81 5) Simplify (a/25) 3/2
9 Warm-Up: Final Review #9 1) Find line perpendicular to 4x + 3y = -2 and through (5, 5) 2) Simplify 50 8 and 3 i 3 i 3) Solve x 2 4x = 9 4) Solve 7x 2 2 = 5x
10 Warm-Up: Final Review #10 1) Simplify 2 6i 2 2) Describe the roots of 3 2x 3x 8 0 3) Find the sum and product of the roots of x 8x 2x 9 0
11 Warm-Up: Final Review #11 1) Find the roots of y = (x + 2)(3x 1) 2) Solve f(x) = x 4-4x ) List the possible rational roots of f ( x) 3x 2x 9x 3x 14 4) Write the equation of the ellipse 2 2 9x 4y 126x 64y 661 0
12 Warm-Up: Final Review #12 1) Write an equation of hyperbola Write equations of asymptotes. V ( 1,0) F 2,0 2) Graph 2 2 x 2 y Name vertices, foci, and equations of asymptotes.
13 Warm-Up: Final Review #13 1) Find the vertex of y = (x 7) ) What is the vertical asymptote of f(x) = 7 2x 1 3) Find the equation of the circle with center at (6, 9) and radius 5. 4) Find the center of the hyperbola 2 2 9x y 54x 2y 71 0
14 Warm-Up: Final Review #14 1) Graph Name the center, vertices, co-vertices and foci. 2 x 3 y x 1 y 2 1 2) Graph Name 25 9 the center, vertices, foci and equations of the asymptotes. 2
15 Warm-Up: Final Review #15 1) f(x) = x 2 +2x g(x) = x - 3, find f(g(x)) 2) If f(x) = x + 4 find the rule for f -1 (x) 3) How can you decide if a function has an inverse function? 4) Solve f(x) = x 4 4x ) Find all the possible rational roots of x 3x 18x 3x 8 0 Is x + 2 a root?
16 Warm-Up: Final Review #16 1) Write 4 3 =64 as a log 2) Evaluate log x 64 = 3 3) Evaluate logn = 4 4) Expand log 5) Compress log525 log53 2 ab c 6) Solve lne 4x =60
17 Warm-Up: Final Review #17 1) Simplify i 33 2) Solve 3 2x-4 =27 x-3 3) Simplify ((x -3 ) 3 ) 0 4) Find the distance, midpoint and slope (4, 6) and (-8, 12)
18 Warm-Up: Final Review #18 1) Find the center of the hyperbola 2 2 x 4y 6x 16y 11 1) Find the vertex of y x a 2 b 2) Find the vertical asymptote of f( x) 5 3x 2
19 Warm-Up: Final Review #19 Convert 1) to DMS 2) to DD 3) 135 to Radians 4) 5 to Degrees 3
20 Warm-Up: Final Review #20 1) The sides of an isosceles triangle are 5, 10, 10. Find all the angle measures. 2) A = 45º, B = 60º, a = 14. Use the law of sines to find the missing measures.
21 Warm-Up: Final Review #21 1) Find a positive and negative angle that is 7 coterminal with angles -35 and 12 2) Convert 300 into radians in terms of pi and to the nearest hundredth of a radian. 3) Convert 1.3 radians to DMS.
22 Warm-Up: Final Review #22 1) Complete the following Pythagorean Identity: csc 2 A = 2) Simplify cotx(sinx) 3) Simplify sin(-x) 4) Name an angle coterminal to 5) Convert to radians. 6) A circle of radius r has a central angle of 30 that subtends an arc of 12. Find the radius. 6
23 Warm-Up: Final Review #23 1) f(x) = 3sinx, find f(-30 ) 2) Find x in radians if tanx = ) Evaluate sincos -1 (-2/7) 4) Evaluate csc 5 3 5) What is the range of f(x) = sinx 6) Describe the movement/change of y 3 2sin 3 x 2
24 Warm-Up: Final Review #24 1) Convert to radians. 2) Solve: secx sinx = 2sinx 3) Solve: 3tanx + 5 = 2 4) Evaluate 5) Find amplitude and period: y = 2sin3x 6) Simplify tan 1 1 sin cos x cot x sin x 1 ( 1 ) 2
25 Warm-Up: Final Review #25 Find the EXACT value of each. 1. cos 5 2. csc sin sec cos (-300) 6. sin 7. tan cot (-π) 9. sec csc (0 ) 11. sin (Tan -1 ( )) tan (Cos -1 ( )) 3 3
26 Warm-Up: Final Review #26 1) Find the exact value for all six trig functions for ) Find all six trig functions of an angle whose terminal ray goes through the point 5, 2 3) Sketch sine, cos, tan. What is the domain, range and zeros for each?
27 Warm-Up: Final Review #27 1) Find the area of a sector of a circle with central angle 30 and arc length 3.5 cm. 2) The diameter of the moon is 3500 km. The apparent size is radians. How far away is the moon from earth? 3) Find sin Θ and cos Θ of an angle whose terminal ray goes through the point 3, 1
28 Warm-Up: Final Review #28 1) Solve sin2x = 1 2) Find cosa if sina = -1/5 and tan < 0. 3) A man is 6 feet tall and casts a shadow 14 feet long. Find the angle of elevation of the sun. 4) Given an oblique triangle with C = 72, A = 15, and b = 342.8, find side a to two decimal places. 5) If sin A = 0.8, and sin B = 0.4 and b = 100, find a.
29 Warm-Up: Final Review #29 1) In triangle ABC, a = 80, b = 51, c = 113. Find measure of angle C. 2) Find sinx given cos(90-x) = ¾ 3) Find sin 15 4) Simplify 5) Simplify tan82 tan12 1 (tan82 )(tan12 sin 2A 2sin A )
30 Warm-Up: Final Review #30 1) Convert (-4, 4) to polar 7 6 2) Convert (-2, ) to rectangular 3) Convert 8-15i to polar 4) Convert 5 cis 120º to rectangular 5) Find z 1 z 2 if z 1 = 6cis150º and z 2 = 1/3cis30º
31 Warm-Up: Final Review #31 1) To convert polar to rectangular let y =? 2) To convert rectangular to polar let Θ =? 3) The coordinate system to graph a complex number is called the?
32 Warm-Up: Final Review #32 1) Express 4(cos30+isin30) in rectangular form 2) Rewrite -7i in polar form 3) Find z 1 z 2 if z1 = (7, 10 ) and z2 = (4, 70 )
33 Warm-Up: Final Review #33 1) Convert (-4, 4) to polar 7 2) Convert (-2, ) to rectangular 3) Convert 8-15i to polar 6 4) Convert 5 cis 120º to rectangular 5) Find z 1 z 2 if z 1 = 6cis150º and z 2 = 1/3cis30º
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 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 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 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 informationWalt Whitman High School SUMMER REVIEW PACKET. For students entering AP CALCULUS BC
Walt Whitman High School SUMMER REVIEW PACKET For students entering AP CALCULUS BC Name: 1. This packet is to be handed in to your Calculus teacher on the first day of the school year.. All work must be
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 informationReview of Trigonometry
Worksheet 8 Properties of Trigonometric Functions Section Review of Trigonometry This section reviews some of the material covered in Worksheets 8, and The reader should be familiar with the trig ratios,
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 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 informationUnit 13: Periodic Functions and Trig
Date Period Unit 13: Periodic Functions and Trig Day Topic 0 Special Right Triangles and Periodic Function 1 Special Right Triangles Standard Position Coterminal Angles 2 Unit Circle Cosine & Sine (x,
More informationCommon Core Standards Addressed in this Resource
Common Core Standards Addressed in this Resource N-CN.4 - Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular
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 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 informationTrigonometry 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 informationAppendix D Trigonometry
Math 151 c Lynch 1 of 8 Appendix D Trigonometry Definition. Angles can be measure in either degree or radians with one complete revolution 360 or 2 rad. Then Example 1. rad = 180 (a) Convert 3 4 into degrees.
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 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 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 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 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 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 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 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 informationObjective: Manipulate trigonometric properties to verify, prove, and understand trigonmetric relationships.
Objective: Manipulate trigonometric properties to verify, prove, and understand trigonmetric relationships. Apr 21 4:09 AM Warm-up: Determine the exact value of the following (without a calculator): sin
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 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 informationLook up partial Decomposition to use for problems #65-67 Do Not solve problems #78,79
Franklin Township Summer Assignment 2017 AP calculus AB Summer assignment Students should use the Mathematics summer assignment to identify subject areas that need attention in preparation for the study
More informationWarm Up: please factor completely
Warm Up: please factor completely 1. 2. 3. 4. 5. 6. vocabulary KEY STANDARDS ADDRESSED: MA3A2. Students will use the circle to define the trigonometric functions. a. Define and understand angles measured
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 informationAP Calculus Summer Review Packet School Year. Name
AP Calculus Summer Review Packet 016-017 School Year Name Objectives for AP/CP Calculus Summer Packet 016-017 I. Solving Equations & Inequalities (Problems # 1-6) Using the properties of equality Solving
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 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 informationAP Calculus Summer Review Packet
AP Calculus Summer Review Packet Name: Date began: Completed: **A Formula Sheet has been stapled to the back for your convenience!** Email anytime with questions: danna.seigle@henry.k1.ga.us Complex Fractions
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 informationMAC Learning Objectives. Learning Objectives (Cont.) Module 2 Acute Angles and Right Triangles
MAC 1114 Module 2 Acute Angles and Right Triangles Learning Objectives Upon completing this module, you should be able to: 1. Express the trigonometric ratios in terms of the sides of the triangle given
More informationIn a right triangle, the sum of the squares of the equals the square of the
Math 098 Chapter 1 Section 1.1 Basic Concepts about Triangles 1) Conventions in notation for triangles - Vertices with uppercase - Opposite sides with corresponding lower case 2) Pythagorean theorem In
More informationProving Trigonometric Identities
MHF 4UI Unit 7 Day Proving Trigonometric Identities An identity is an epression which is true for all values in the domain. Reciprocal Identities csc θ sin θ sec θ cos θ cot θ tan θ Quotient Identities
More informationTrigonometry Summer Assignment
Name: Trigonometry Summer Assignment Due Date: The beginning of class on September 8, 017. The purpose of this assignment is to have you practice the mathematical skills necessary to be successful in Trigonometry.
More informationMath 1330 Test 3 Review Sections , 5.1a, ; Know all formulas, properties, graphs, etc!
Math 1330 Test 3 Review Sections 4.1 4.3, 5.1a, 5. 5.4; Know all formulas, properties, graphs, etc! 1. Similar to a Free Response! Triangle ABC has right angle C, with AB = 9 and AC = 4. a. Draw and label
More informationDate Lesson Text TOPIC Homework. Getting Started Pg. 314 # 1-7. Radian Measure and Special Angles Sine and Cosine CAST
UNIT 5 TRIGONOMETRIC FUNCTIONS Date Lesson Text TOPIC Homework Oct. 0 5.0 (50).0 Getting Started Pg. # - 7 Nov. 5. (5). Radian Measure Angular Velocit Pg. 0 # ( 9)doso,,, a Nov. 5 Nov. 5. (5) 5. (5)..
More information4.1 Angles and Angle Measure. 1, multiply by
4.1 Angles and Angle Measure Angles can be measured in degrees or radians. Angle measures without units are considered to be in radians. Radian: One radian is the measure of the central angle subtended
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 informationIB SL Review Questions
I SL Review Questions. Solve the equation 3 cos x = 5 sin x, for x in the interval 0 x 360, giving your answers to the nearest degree.. Given that sin θ =, cos θ = 3 and 0 < θ < 360, find the value of
More informationName Trigonometric Functions 4.2H
TE-31 Name Trigonometric Functions 4.H Ready, Set, Go! Ready Topic: Even and odd functions The graphs of even and odd functions make it easy to identify the type of function. Even functions have a line
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 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 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 informationMATHEMATICS 105 Plane Trigonometry
Chapter I THE TRIGONOMETRIC FUNCTIONS MATHEMATICS 105 Plane Trigonometry INTRODUCTION The word trigonometry literally means triangle measurement. It is concerned with the measurement of the parts, sides,
More informationMA 154 Lesson 1 Delworth
DEFINITIONS: An angle is defined as the set of points determined by two rays, or half-lines, l 1 and l having the same end point O. An angle can also be considered as two finite line segments with a common
More informationPre-Calculus Summer Assignment
Name: Pre-Calculus Summer Assignment Due Date: The beginning of class on September 8, 017. The purpose of this assignment is to have you practice the mathematical skills necessary to be successful in Pre-Calculus.
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 informationTrigonometry Curriculum Guide Scranton School District Scranton, PA
Trigonometry Scranton School District Scranton, PA Trigonometry Prerequisite: Algebra II, Geometry, Algebra I Intended Audience: This course is designed for the student who has successfully completed Algebra
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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
E. McGann LA Mission College Math 125 Fall 2014 Test #1 --> chapters 3, 4, & 5 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate
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 informationSec 4.1 Trigonometric Identities Basic Identities. Name: Reciprocal Identities:
Sec 4. Trigonometric Identities Basic Identities Name: Reciprocal Identities: Quotient Identities: sin csc cos sec csc sin sec cos sin tan cos cos cot sin tan cot cot tan Using the Reciprocal and Quotient
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 informationThe Sine and Cosine Functions
Concepts: Graphs of Tangent, Cotangent, Secant, and Cosecant. We obtain the graphs of the other trig functions by thinking about how they relate to the sin x and cos x. The Sine and Cosine Functions Page
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 informationHW#50: Finish Evaluating Using Inverse Trig Functions (Packet p. 7) Solving Linear Equations (Packet p. 8) ALL
MATH 4R TRIGONOMETRY HOMEWORK NAME DATE HW#49: Inverse Trigonometric Functions (Packet pp. 5 6) ALL HW#50: Finish Evaluating Using Inverse Trig Functions (Packet p. 7) Solving Linear Equations (Packet
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 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 informationCURRICULUM MAP. Course / Subject: Precalculus Grade: 11/12 Teacher: Kelly, Kirk, McCollick, Palkovics, Roderick Month: September (19 days)
Month: September (19 days) - Change from radian to degree measure, & vice versa - Find angles that are coterminal with a given angle - Find reference angle for a given angle Angles & Their Measure (Section
More informationTrigonometry I. Exam 0
Trigonometry I Trigonometry Copyright I Standards 006, Test Barry Practice Mabillard. Exam 0 www.math0s.com 1. The minimum and the maximum of a trigonometric function are shown in the diagram. a) Write
More informationName:& &Date:& &Block:& & & &
Name: Date: Block: Advanced(Math(Mid-Term(Review((short)( ( Evaluatethefollowingexpressionsusingthetrianglegivenbelow.Expressanswers insimplifiedfractionalform.(nosquarerootsinthedenominator) 1. ( ( Solvefortheindicatedvariable(s)onthefollowingtriangles.Showallworkand
More informationPacket Unit 5 Trigonometry Honors Math 2 17
Packet Unit 5 Trigonometry Honors Math 2 17 Homework Day 12 Part 1 Cumulative Review of this unit Show ALL work for the following problems! Use separate paper, if needed. 1) If AC = 34, AB = 16, find sin
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 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 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 informationA Quick Review of Trigonometry
A Quick Review of Trigonometry As a starting point, we consider a ray with vertex located at the origin whose head is pointing in the direction of the positive real numbers. By rotating the given ray (initial
More informationTrigonometric Functions of Any Angle
Trigonometric Functions of Any Angle MATH 160, Precalculus J. Robert Buchanan Department of Mathematics Fall 2011 Objectives In this lesson we will learn to: evaluate trigonometric functions of any angle,
More informationMidterm Review January 2018 Honors Precalculus/Trigonometry
Midterm Review January 2018 Honors Precalculus/Trigonometry Use the triangle below to find the exact value of each of the trigonometric functions in questions 1 6. Make sure your answers are completely
More information1. The Pythagorean Theorem
. The Pythagorean Theorem The Pythagorean theorem states that in any right triangle, the sum of the squares of the side lengths is the square of the hypotenuse length. c 2 = a 2 b 2 This theorem can be
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 information17-18 CP Geometry Final Exam REVIEW
1 17-18 CP Geometry Final Exam REVIEW Identify the scale factor of each dilation. 1. 2. Dilate the following given each scale factor. Be sure to label the images properly. 1 3. Scale factor of 4 4. Scale
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 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 informationa. b. c. d. e. f. g. h.
Sec. Right Triangle Trigonometry Right Triangle Trigonometry Sides Find the requested unknown side of the following triangles. Name: a. b. c. d.? 44 8 5? 7? 44 9 58 0? e. f. g. h.?? 4 7 5? 38 44 6 49º?
More informationMATH 1113 Exam 3 Review. Fall 2017
MATH 1113 Exam 3 Review Fall 2017 Topics Covered Section 4.1: Angles and Their Measure Section 4.2: Trigonometric Functions Defined on the Unit Circle Section 4.3: Right Triangle Geometry Section 4.4:
More informationPre-calculus: 1st Semester Review Concepts Name: Date: Period:
Pre-calculus: 1st Semester Review Concepts Name: Date: Period: Problem numbers preceded by a $ are those similar to high miss questions on the Semester Final last year. You have multiple resources to study
More informationUse Trigonometry with Right Triangles SECTION 13.1
Use Trigonometry with Right Triangles SECTION 13.1 WARM UP In right triangle ABC, a and b are the lengths of the legs and c is the length of the hypotenuse. Find the missing length. Give exact values (leave
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 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 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 informationFAIRFIELD COUNTY MATH LEAGUE (FCML) )Find the arithmetic mean of the median and the mode of the numbers {13, 23, 24, 24, 15, 18, 24, 22}.
FAIRFIELD COUNTY MATH LEAGUE (FCML)2015-2016 Match 4 Round 1 Arithmetic: Basic Statistics 1.) 2.25 2.) 6.) 18 1.)Find the arithmetic mean of the median and the mode of the numbers {1, 2, 24, 24, 15, 18,
More informationPre-calculus Chapter 4 Part 1 NAME: P.
Pre-calculus NAME: P. Date Day Lesson Assigned Due 2/12 Tuesday 4.3 Pg. 284: Vocab: 1-3. Ex: 1, 2, 7-13, 27-32, 43, 44, 47 a-c, 57, 58, 63-66 (degrees only), 69, 72, 74, 75, 78, 79, 81, 82, 86, 90, 94,
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 informationLESSON 1: Trigonometry Pre-test
LESSON 1: Trigonometry Pre-test Instructions. Answer each question to the best of your ability. If there is more than one answer, put both/all answers down. Try to answer each question, but if there is
More informationMath 144 Activity #2 Right Triangle Trig and the Unit Circle
1 p 1 Right Triangle Trigonometry Math 1 Activity #2 Right Triangle Trig and the Unit Circle We use right triangles to study trigonometry. In right triangles, we have found many relationships between the
More information5.5 Multiple-Angle and Product-to-Sum Formulas
Section 5.5 Multiple-Angle and Product-to-Sum Formulas 87 5.5 Multiple-Angle and Product-to-Sum Formulas Multiple-Angle Formulas In this section, you will study four additional categories of trigonometric
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 informationPre-Calc Trig ~1~ NJCTL.org. Unit Circle Class Work Find the exact value of the given expression. 7. Given the terminal point ( 3, 2 10.
Unit Circle Class Work Find the exact value of the given expression.. cos π. tan 5π 6. sin 7π 5. cot 5π. sec π 6. csc 9π 7. Given the terminal point (, 0 ) find tanθ 7 tan θ = 0 7 8. Given the terminal
More informationSolving Trigonometric Equations
OpenStax-CNX module: m49398 1 Solving Trigonometric Equations OpenStax College This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section, you
More informationSolving Right Triangles. How do you solve right triangles?
Solving Right Triangles How do you solve right triangles? The Trigonometric Functions we will be looking at SINE COSINE TANGENT The Trigonometric Functions SINE COSINE TANGENT SINE Pronounced sign TANGENT
More information5. The angle of elevation of the top of a tower from a point 120maway from the. What are the x-coordinates of the maxima of this function?
Exams,Math 141,Pre-Calculus, Dr. Bart 1. Let f(x) = 4x+6. Find the inverse of f algebraically. 5x 2. Suppose f(x) =x 2.We obtain g(x) fromf(x) by translating to the left by 2 translating up by 3 reecting
More informationRewrite the equation in the left column into the format in the middle column. The answers are in the third column. 1. y 4y 4x 4 0 y k 4p x h y 2 4 x 0
Pre-Calculus Section 1.1 Completing the Square Rewrite the equation in the left column into the format in the middle column. The answers are in the third column. 1. y 4y 4x 4 0 y k 4p x h y 4 x 0. 3x 3y
More information1. Be sure to complete the exploration before working on the rest of this worksheet.
PreCalculus Worksheet 4.1 1. Be sure to complete the exploration before working on the rest of this worksheet.. The following angles are given to you in radian measure. Without converting to degrees, draw
More informationI \ I I I MATH ANALYSIS I HONORS. REVIEW #I Chapters I and 2. l. Find the equation of the line parallel to 5x - 2y :6 with a y-intercept of 3.
MATH ANALYSS HONORS REVEW # Chapters and 2 l. Find the equation of the line parallel to 5x - 2y :6 with a y-intercept of 3. 2. Find the point of intersection betweenthe lines 2x-2y - -6 and 5x +y:21. 3.
More informationLesson 27: Angles in Standard Position
Lesson 27: Angles in Standard Position PreCalculus - Santowski PreCalculus - Santowski 1 QUIZ Draw the following angles in standard position 50 130 230 320 770-50 2 radians PreCalculus - Santowski 2 Fast
More informationP1 REVISION EXERCISE: 1
P1 REVISION EXERCISE: 1 1. Solve the simultaneous equations: x + y = x +y = 11. For what values of p does the equation px +4x +(p 3) = 0 have equal roots? 3. Solve the equation 3 x 1 =7. Give your answer
More information