Review Exercises for Chapter 4

Similar documents
Chapter Summary. What did you learn? 364 Chapter 4 Trigonometry

Precalculus Lesson 6.1: Angles and Their Measure Lesson 6.2: A Unit Circle Approach Part 2

I. Degrees and Radians minutes equal 1 degree seconds equal 1 minute. 3. Also, 3600 seconds equal 1 degree. 3.

CHAPTER 6. Section Two angles are supplementary. 2. Two angles are complementary if the sum of their measures is 90 radians

CHAPTER 4 Trigonometry

Precalculus A - Final Exam Review Fall, 2014

Chapter 11. Graphs of Trigonometric Functions

I IV II III 4.1 RADIAN AND DEGREE MEASURES (DAY ONE) COMPLEMENTARY angles add to90 SUPPLEMENTARY angles add to 180

(c) cos Arctan ( 3) ( ) PRECALCULUS ADVANCED REVIEW FOR FINAL FIRST SEMESTER

A List of Definitions and Theorems

4-3 Trigonometric Functions on the Unit Circle

REVIEW, pages

Math Section 4.3 Unit Circle Trigonometry

Math 107 Study Guide for Chapters 5 and Sections 6.1, 6.2 & 6.5

Ch 5 and 6 Exam Review

Math 175: Chapter 6 Review: Trigonometric Functions

( 3 ) = (r) cos (390 ) =

Mth 133 Trigonometry Review Problems for the Final Examination

CK- 12 Algebra II with Trigonometry Concepts 1

Section 6.1 Angles and Radian Measure Review If you measured the distance around a circle in terms of its radius, what is the unit of measure?

Practice Test - Chapter 4

Find: sinθ. Name: Date:

Chapter 4 Trigonometric Functions

1.1 Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 1) 162

Practice Questions for Midterm 2 - Math 1060Q Fall

From now on angles will be drawn with their vertex at the. The angle s initial ray will be along the positive. Think of the angle s

(Section 4.7: Inverse Trig Functions) 4.82 PART F: EVALUATING INVERSE TRIG FUNCTIONS. Think:

Math Section 4.3 Unit Circle Trigonometry

Trigonometry Final Exam Review

Trigonometric Identities Exam Questions

Trigonometry 1st Semester Review Packet (#2) C) 3 D) 2

Math 1303 Part II. The opening of one of 360 equal central angles of a circle is what we chose to represent 1 degree

Analytic Trigonometry

PRECALCULUS FINAL EXAM REVIEW

Algebra II B Review 5

1. State the amplitude and period for the function y = -3 sin 3. 3 * theta = 2* pi (Because, 2*pi is period for sine function

Section 6.1 Sinusoidal Graphs

Exercise Set 4.3: Unit Circle Trigonometry

Solutions to Some Additional Practice for the Midterm Exam

9.1 Practice A. Name Date sin θ = and cot θ = to sketch and label the triangle. Then evaluate. the other four trigonometric functions of θ.

Chapter 5 Notes. 5.1 Using Fundamental Identities

Unit #17: Spring Trig Unit. A. First Quadrant Notice how the x-values decrease by while the y-values increase by that same amount.

1. (10pts) If θ is an acute angle, find the values of all the trigonometric functions of θ given that tan θ = 1. Draw a picture.

MATH 1316 REVIEW FOR FINAL EXAM

6.5 Trigonometric Equations

1.1 Angles and Degree Measure

Final Exam Review Problems

Chapter 1: Trigonometric Functions 1. Find (a) the complement and (b) the supplement of 61. Show all work and / or support your answer.

Section 6.2 Notes Page Trigonometric Functions; Unit Circle Approach

Section 6.2 Trigonometric Functions: Unit Circle Approach

Functions & Trigonometry Final Review #3. 3. Please find 2 coterminal angels (one positive and one negative) in the same measure as the given angle.

Given an arc of length s on a circle of radius r, the radian measure of the central angle subtended by the arc is given by θ = s r :

CHAPTER 5: Analytic Trigonometry

Pre-Calculus Semester 1 Practice Final

Chapter 6: Periodic Functions

Pre-Calculus II: Trigonometry Exam 1 Preparation Solutions. Math&142 November 8, 2016

Given one trigonometric ratio and quadrant, determining the remaining function values

CHAPTER 3 Applications of Differentiation

Unit 5 PreCalculus Review

Name Date Period. Calculater Permitted MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. and θ is in quadrant IV. 1)

MATH 1113 A Review for Exam 1 Solution. 1. For the next few questions, consider the function. b. What is the domain of f? All real numbers except 3

Pre-Exam. 4 Location of 3. 4 sin 3 ' = b Location of 180 ' = c Location of 315

MATH 130 FINAL REVIEW

Trigonometric Functions. Copyright Cengage Learning. All rights reserved.

* Circle these problems: 23-27, 37, 40-44, 48, No Calculator!

6.1 Reciprocal, Quotient, and Pythagorean Identities.notebook. Chapter 6: Trigonometric Identities

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 4) cot! sec! sin! 4) 6) sin! cos! sec! csc!

Fundamentals of Mathematics (MATH 1510)

Section Inverse Trigonometry. In this section, we will define inverse since, cosine and tangent functions. x is NOT one-to-one.

Group/In-Class Exercises 8/18/09 g0401larson8etrig.tst 4.1 Radian and Degree Measure

Section 6.1. Standard position- the vertex of the ray is at the origin and the initial side lies along the positive x-axis.

Practice Questions for Midterm 2 - Math 1060Q - Fall 2013

2.Draw each angle in standard position. Name the quadrant in which the angle lies. 2. Which point(s) lies on the unit circle? Explain how you know.

MIDTERM 3 SOLUTIONS (CHAPTER 4) INTRODUCTION TO TRIGONOMETRY; MATH 141 SPRING 2018 KUNIYUKI 150 POINTS TOTAL: 30 FOR PART 1, AND 120 FOR PART 2

Sect 7.4 Trigonometric Functions of Any Angles

Unit 4 Example Review. 1. Question: a. [A] b. [B] c. [C] d. [D]

Chapter 6. Trigonometric Functions of Angles. 6.1 Angle Measure. 1 radians = 180º. π 1. To convert degrees to radians, multiply by.

Practice Test - Chapter 4

Since 1 revolution = 1 = = Since 1 revolution = 1 = =

Directions: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies.

Lesson 10.2 Radian Measure and Arc Length

TOTAL NAME DATE PERIOD AP CALCULUS AB UNIT 4 ADVANCED DIFFERENTIATION TECHNIQUES DATE TOPIC ASSIGNMENT /6 10/8 10/9 10/10 X X X X 10/11 10/12

Algebra II Standard Term 4 Review packet Test will be 60 Minutes 50 Questions

Trigonometry Exam 2 Review: Chapters 4, 5, 6

MATH 127 SAMPLE FINAL EXAM I II III TOTAL

NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part 2 Trigonometry, 10th Edition; Lial, Hornsby, Schneider Spring 2013

CHAPTER 3 Applications of Differentiation

PART I: NO CALCULATOR (144 points)

Chapter 5. Section 5.1. Section ( x ) ( y ) 7. ( x ) ( y ) (0, 3 + 5) and (0, 3 5)

Unit 4 Example Review. 1. Question: a. [A] b. [B] c. [C] d. [D]

Chapter 5: Trigonometric Functions of Angles Homework Solutions

The function is a periodic function. That means that the functions repeats its values in regular intervals, which we call the period.

Given an arc of length s on a circle of radius r, the radian measure of the central angle subtended by the arc is given by θ = s r :

Chapter 11B: Trig Graphing Review Sheet Test Wednesday 05/17/2017

Chapter 1 Prerequisites for Calculus

Lesson 28 Working with Special Triangles

a) Draw the angle in standard position. b) determine an angle that is co-terminal to c) Determine the reference angle of

1 x. II. CHAPTER 2: (A) Graphing Rational Functions: Show Asymptotes using dotted lines, Intercepts, Holes(Coordinates, if any.)

Unit 3 Trigonometry. 3.4 Graph and analyze the trigonometric functions sine, cosine, and tangent to solve problems.

Transcription:

0 Chapter Trigonometr Review Eercises for Chapter. 0. radian.. radians... The angle lies in Quadrant II. (c) Coterminal angles: Quadrant I (c) 0 The angle lies in Quadrant II. (c) Coterminal angles: 0. 7. 708. 80 70 80 Quadrant I (c) 8 7 The angle lies in Quadrant I. (c) Coterminal angles: 70 0 0 70 0 0 Quadrant IV (c) 80 0 0 80 0 80

Review Eercises for Chapter. 00. 0. 80 80 rad 80 8 radians 0 8.78 radians 0 The angle lies in Quadrant III. (c) Coterminal angles: 0 0 0 Quadrant IV (c) 0 70 0 0 0 0 70. 7... 80.7.7 rad 80 radian 0.8 radian. 77 77 0 80.. rad 7 rad 7 80 rad 8.7. 80 0.000 7.. rad. rad 80 rad 00. 8..7 80.8. 8 8 radians 80 0 0. s r 0 0 8.7 inches 0 0 80 radians s r 0 80 meters s. meters. Angular speed radians minute radians per minute Linear speed inches minute 00 inches per minute. linear speed angular speed radius rads. inches 7. inches per second. inches per second.0 miles per hour. 0 0 radians 80 A r 8. square inches. A r. A. square millimeters. t corresponds to the point.,. t,,,

Chapter Trigonometr 7. t corresponds to the point,. 7. t corresponds to the point 7 sin cos 7 7 tan,. csc 7 sec 7 cot 7 8. t,,, 0. t corresponds to the point sin cos tan csc sec,. cot. t corresponds to the point sin cos tan,. csc sec cot. t corresponds to the point, 0. sin 0 csc is undefined. cos sec tan 0 cot is undefined.. sin sin. cos cos 0. sin 7 sin. cos cos 7. tan 7.0 8. csc 0..8 sin 0.. sec cos. 0. sin 0.0. opp, adj, hp. adj, opp sin opp hp cos adj hp tan opp adj csc hp opp sec hp adj cot adj opp hp sin opp hp cos adj hp tan opp adj csc hp opp sec hp adj cot adj opp. adj, hp 8, opp 8 8 sin opp hp 8 cos adj hp 8 tan opp adj csc hp opp 8 sec hp adj 8 cot adj opp

Review Eercises for Chapter. opp, hp. adj sin opp hp cos adj hp tan opp adj 8 csc hp opp sec hp adj 8 cot adj opp sin (c) csc sin sin cos cos cos cos 8 cos 8 cos sec cos (d) tan sin cos. tan 7. (c) cot tan sec tan 7 cos 7 sec 7 7 (d) csc cot 7 csc sin csc sin cos cos cos cos cos cos (c) sec cos (d) tan sin cos 8. csc sin csc cot csc (c) tan cot (d) sec0 csc. tan 0. 0. csc.08. sin. 0. sin

Chapter Trigonometr. sec 7. cos 7..80. cot tan 0.7. cos 78 8 cos 78 0.0 0 8 00. sin 0.. sin 0 0.07 kilometer or 7. meters. km 0' Not drawn to scale. tan. feet tan 7.,, r 00 0 8. sin r csc r,, r sin r csc r cos r sec r cos r sec r tan cot tan cot., r sin r cos r tan csc r sec r cot 0 0., 0, r 0 sin r cos r tan 0 0 csc r sec r cot 0 0

Review Eercises for Chapter. 0.,. r 0.. 0. 8 sin r cos r tan. 8 8 8 0. 8 8 8. 0. csc r sec r cot 8. 8 0. 8 0.. 8., 0., 0. r 0. 0. 0. sin r cos r tan 0. 0. 0.8 0. 0. 0. 0. 0.. csc r sec r cot 0. 0.. 0. 0..7 0. 0. 0.7.,, > 0, r 7 sin r 7 7 7 cos r 7 7 7 tan csc r 7 7 sec r 7 7 cot.,,, > 0. sec is in Quadrant IV., tan < 0 r sin r cos r tan csc r sec r cot r,, sin r cos r tan csc r sec cot

Chapter Trigonometr. csc, cos < 0 7. sin is in Quadrant II. 8, cos < 0 is in Quadrant II. sin csc cos sin tan sin cos sec cos cot tan, r 8, sin r 8 cos r tan csc 8 sec 8 8 cot 8 8. tan, cos < 0. is in Quadrant III. sec tan cos r sin > 0 sin r is in Quadrant II cos sec sin cos csc sin cot tan tan csc r sec r cot 70. sin, cos > 0 7. is in Quadrant IV. csc sin cos sin sec cos 80 8 θ tan sin cos cot tan

Review Eercises for Chapter 7 7. 70 87. 8 7. 7 8 θ θ 7 θ 7. sin 7. sin 77. sin 7 sin cos cos cos 7 cos tan tan tan 7 tan 78. sin sin cos cos 7. sin sin cos cos 80. sin0 cos0 tan tan tan tan tan0 8. sin0 sin 0 8. sin cos0 cos 0 cos tan0 tan 0 tan 8. sin 0.78 8. tan 0. 8. sin. 0.08 8. cot.8 tan.8 0.0878 87. sec cos. 88. tan 7.8

8 Chapter Trigonometr 8. sin 0. cos. Amplitude: Amplitude: f sin Amplitude:. f 8 cos. sin. cos Amplitude: 8 8 8 Shift the graph of sin two units upward. Amplitude: 8 8. gt sint. gt cost 7. a sin b Amplitude: t Amplitude: t a, b b 8 sin8 f ccles per second. 8. St 8.0. sin t.0 0 Period months ear, so this is epected. (c) Amplitude:. The amplitude represents the maimum change in the time of sunset from the average time d 8.0.

Review Eercises for Chapter. f tan 00. f t tan t 0. f cot t 0. gt cot t 0. f sec 0. Graph cos first. ht sec t t t 0. f csc 0. Graph sin first. f t csc t t 07. f cos 08. g cos 00 Graph and first. As, f. Damping factor: As, f. 00 0. arcsin arcsin 0. arcsin. arcsin 0. 0. radian. arcsin0. 0. radian. sin 0. 0. radian. sin 0.8.0 radians. arccos. arccos 7. cos

0 Chapter Trigonometr 8. cos. arccos 0.. radians 0. arccos0.888. radians. tan. 0.8 radian. tan 8.. radians. f arcsin sin. arccos.... 0. f arctan tan. f arcsin.. 7. cosarctan 8. Let u arccos. Use a right triangle. Let then tan and cos. arctan θ tanarccos tan u u. secarctan 0. Let Use a right triangle. Let then tan and sec arctan. u arcsin. cot arcsin cot u u θ. Let arccos Then.. secarcsin cos and tan tan arccos. arcsin sin sec cos θ ( )

Review Eercises for Chapter. tan 70 0 arctan 70.8 0. tan h h tan. feet h. sin 8 d 0 d 8 cos d 80 d 7 cos 8 d 0 d sin d 80 d tan 7. d d 7 d d N W 8 B 8 d 80 d 0 D C A θ d d S E sec. D 7 D 7 sec. The distance is miles and the bearing is 8.... Amplitude: 0.7 inches 7. False. The sine or cosine functions are often useful for modeling seconds simple harmonic motion. d a cos bt a 0.7 b d 0.7 cos t 8. True. The inverse sine, arcsin, is defined where and.. False. For each there corresponds eactl one value of. 0. False. The range of arctan is so arctan,.,. sin Amplitude: Matches graph d. sin matches graph.. Amplitude: sin. sin matches graph (c). Amplitude: Matches graph b Amplitude:. f sec is undefined at the zeros of g cos since sec. cos

Chapter Trigonometr. tan 0. 0. 0.7.0. tan...87 0. 0.77 cot cot...87 0. 0.77 7. The ranges for the other four trigonometric functions are not bounded. For tan and cot, the range is,. For sec and csc, the range is,,. 8. Ae kt cos bt e t0 cos t A is changed from to : The displacement is increased. k is changed from 0 to : The friction damps the oscillations more rapidl. (c) b is changed from to : The frequenc of oscillation is increased.. A r, s r A r 0.8 0.r, r > 0 s r0.8 0.8r, r > 0 As r increases, the area function increases more rapidl. A s A 0 0, > 0 s 0, > 0 0 A s 0 0 0 0 0. Answers will var. Problem Solving for Chapter. 8:7 : hours minutes minutes. Gear : 8 revolutions radians or 0 s r 7.. 8. feet Gear : Gear : Gear : 0 70 radians 0.08.80 radians 0.77.8 radians 0 0 0 radians Gear : 0.77 7. radians. sin 000 d (c) tan w 70 000 d 000 77 feet sin 000 tan w 70 w 000 tan 70 8 feet tan 000 000 70 feet tan