Algebra II B Review 5

Similar documents
4-3 Trigonometric Functions on the Unit Circle

Practice Test - Chapter 4

Trigonometric Identities Exam Questions

Practice Test - Chapter 4

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.

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

CK- 12 Algebra II with Trigonometry Concepts 1

A. Incorrect! For a point to lie on the unit circle, the sum of the squares of its coordinates must be equal to 1.

Math Section 4.3 Unit Circle Trigonometry

Exercise Set 6.2: Double-Angle and Half-Angle Formulas

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

Trigonometric Identity Practice

Section 6.2 Notes Page Trigonometric Functions; Unit Circle Approach

SESSION 6 Trig. Equations and Identities. Math 30-1 R 3. (Revisit, Review and Revive)

PART I: NO CALCULATOR (144 points)

Math Section 4.3 Unit Circle Trigonometry

AFM Midterm Review I Fall Determine if the relation is a function. 1,6, 2. Determine the domain of the function. . x x

Math 175: Chapter 6 Review: Trigonometric Functions

Precalculus A - Final Exam Review Fall, 2014

Chapter 5 Analytic Trigonometry

Exam Review 2 nd Semester 6-1 Operations on Functions

Ch 5 and 6 Exam Review

12) y = -2 sin 1 2 x - 2

Analytic Trigonometry. Copyright Cengage Learning. All rights reserved.

TRIGONOMETRIC FUNCTIONS. Copyright Cengage Learning. All rights reserved.

A2T Trig Packet Unit 1

sin cos 1 1 tan sec 1 cot csc Pre-Calculus Mathematics Trigonometric Identities and Equations

Exercise Set 4.3: Unit Circle Trigonometry

5.3 Properties of Trigonometric Functions Objectives

(C), 5 5, (B) 5, (C) (D), 20 20,

CHAPTERS 5-7 TRIG. FORMULAS PACKET

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 :

MATH 130 FINAL REVIEW

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

MTH30 Review Sheet. y = g(x) BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE

An angle in the Cartesian plane is in standard position if its vertex lies at the origin and its initial arm lies on the positive x-axis.

5-3 Solving Trigonometric Equations

NAME DATE PERIOD. Trigonometric Identities. Review Vocabulary Complete each identity. (Lesson 4-1) 1 csc θ = 1. 1 tan θ = cos θ sin θ = 1

Honors Algebra 2 Chapter 14 Page 1

More with Angles Reference Angles

Lesson 7.3 Exercises, pages

REVIEW, pages

Trigonometry 1 Review for the District Final

Honors PreCalculus Final Exam Review Mr. Serianni

( ) a (graphical) transformation of y = f ( x )? x 0,2π. f ( 1 b) = a if and only if f ( a ) = b. f 1 1 f

Section 6.2 Trigonometric Functions: Unit Circle Approach

2. Determine the domain of the function. Verify your result with a graph. f(x) = 25 x 2

MA40S Pre-calculus UNIT C Trigonometric Identities CLASS NOTES Analyze Trigonometric Identities Graphically and Verify them Algebraically

Unit 5 PreCalculus Review

As we know, the three basic trigonometric functions are as follows: Figure 1

1 Chapter 2 Perform arithmetic operations with polynomial expressions containing rational coefficients 2-2, 2-3, 2-4

6.5 Trigonometric Equations

Lesson 10.2 Radian Measure and Arc Length

NYS Algebra II and Trigonometry Suggested Sequence of Units (P.I's within each unit are NOT in any suggested order)

CHAPTER 5: Analytic Trigonometry

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

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

Using this definition, it is possible to define an angle of any (positive or negative) measurement by recognizing how its terminal side is obtained.

Mth 133 Trigonometry Review Problems for the Final Examination

Precalculus Review. Functions to KNOW! 1. Polynomial Functions. Types: General form Generic Graph and unique properties. Constants. Linear.

CK- 12 Algebra II with Trigonometry Concepts 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.

Math 370 Exam 2 Review Name

C) ) cos (cos-1 0.4) 5) A) 0.4 B) 2.7 C) 0.9 D) 3.5 C) - 4 5

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

MIDTERM 4 PART 1 (CHAPTERS 5 AND 6: ANALYTIC & MISC. TRIGONOMETRY) MATH 141 FALL 2018 KUNIYUKI 150 POINTS TOTAL: 47 FOR PART 1, AND 103 FOR PART

Find: sinθ. Name: Date:

Notes on Radian Measure

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 :

Trigonometry LESSON SIX - Trigonometric Identities I Lesson Notes

Summer Mathematics Prep

Inverse Trig Functions

0615a2. Algebra 2/Trigonometry Regents Exam x 2 y? 4 x. y 2. x 3 y

Algebra II Final Exam Semester II Practice Test

A) 13 B) 9 C) 22 D) log 9

Math 5 Trigonometry Chapter 4 Test Fall 08 Name Show work for credit. Write all responses on separate paper. Do not use a calculator.

Algebra 2, Spring Semester Review

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

Honors Pre-calculus Midterm Review

0610a2. Algebra 2/Trigonometry Regents Exam ) 3 3) 3 4) 9 12? 1) 150 2) 165 3) 330 4) 518. b? 3

Date Period In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest tenth. 12) sec 29p 6

1 The six trigonometric functions

Transition to College Math

TO EARN ANY CREDIT, YOU MUST SHOW STEPS LEADING TO THE ANSWER

4 The Trigonometric Functions

Solve the problem. 2) If tan = 3.7, find the value of tan + tan ( + ) + tan ( + 2 ). A) 11.1 B) 13.1 C) D) undefined

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

122. Period: x 4 2 x 7

Math 1060 Midterm 2 Review Dugopolski Trigonometry Edition 3, Chapter 3 and 4

AP Calculus I Summer Packet

PART 1: USING SCIENTIFIC CALCULATORS (50 PTS.)

9) A) f-1(x) = 8 - x B) f-1(x) = x - 8 C)f-1(x) = x + 8 D) f-1(x) = x 8

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

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

8-2 Trigonometric Ratios

Algebra II CP Final Exam Review Packet. Calculator Questions

A. Incorrect! This equality is true for all values of x. Therefore, this is an identity and not a conditional equation.

6.1: Reciprocal, Quotient & Pythagorean Identities

Chapter 4/5 Part 1- Trigonometry in Radians

Transcription:

Algebra II B Review 5 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the measure of the angle below. y x 40 ο a. 135º b. 50º c. 310º d. 270º Sketch the angle in standard position. 2. 140º a. y c. y 140 ο x 140 ο x

b. y d. y 140 ο x 140 ο x 3. Find the cosine and sine of 90º. Round your answers to the nearest hundredth if necessary. y 90 ο x a. 0.71, 0.71 b. 0, 1 c. 0.71, 0.71 d. 1.1, 0 4. Find the exact value of cos 300º and sin 300º. b. d. Write the measure in radians. Express the answer in terms of π. 5. 140º a. b. c. d. 6. 45º a. b. c. d. Write the measure in degrees.

7. radians a. 300º b. º c. 5.24º d. º 8. radians a. º b. 144º c. 2.51º d. º Use the graph of y = sin θ to find the value of sin θ for each value of θ. 9. 360º a. 0.4 b. 0.2 c. 0 d. 0.6 10. 5 3 radians a. 0.7 b. 0.3 c. 0.9 d. 0.5 11. Find the period of the graph shown below.

a. 2π b. 2 3 π c. 1 2 π d. π 12. Find the amplitude of the sine curve shown below. a. 2π b. 1 c. 0.5 d. 2 13. Sketch one cycle of y = 3 sin 3θ.

b. d. 14. Write the equation for the sine function shown below. b. d. 15. Find the period, range, and amplitude of the cosine function. a. b. c. d. Write a cosine function for the graph.

16. b. d. 17. Use a graphing calculator to solve the equation in the interval from 0 to 2π. Round to the nearest hundredth. a. 2.41, 4.17 c. 2.30, 3.98 b. 2.20, 4.09 d. 3.80, 2.20, 2.20, 3.80 18. Write an equation of the cosine function with amplitude 2 and period 4π. b. d. 19. Use the graph of to find the value of y = tan 1 π. Round to the nearest tenth if necessary. If the 4 tangent is undefined at that point, write undefined. a. 0.4 b. 1 c. 0 d. 2.4

20. Sketch the graph of the tangent curve y = tan 1 4 in the interval from 0 to 2π. b. d. 21. Use a graphing calculator to graph the function on the interval and. Evaluate the function at. Round to the nearest tenth. a. 1.7, 1.7, 0 c. 225.2, 225.2, 0 b. 225.2, 225.2, 0 d. 225.2, 225.2, 0 22. Use the function y = 50 tan x on the interval. Complete the ordered pair (x, 125). Round your answer to the nearest whole number. a. 90º b. 22º c. 2º d. 68º 23. Use a graphing calculator to solve the equation in the interval from. Round your answers to the nearest hundredth. a. 1.21, 4.35 c. 1.21, 2.26, 3.31, 4.35, 5.40 b. 3.64 d. 0.404, 1,452.5, 3.55, 4.59, 5.64 24. Identify the period for and tell where two asymptotes occur for the function. a. period = ; two asymptotes at x = and x =

b. c. d. period = ; two asymptotes at x = and x = period = ; two asymptotes at x = and x = 2 period = ; two asymptotes at x = 0 and x = Graph the function in the interval from 0 to 2π. 25. y = 4 cos 4θ b. d. 26. Evaluate cot 105º. Round your answer to the nearest hundredth. a. 1.04 b. 0.27 c. 3.73 d. 3.86 27. Suppose. Find. a. b. c. d. 176 28. Find the exact value of csc 135º. If the expression is undefined, write undefined. a. 0 b. undefined c. d.

29. Find the exact value of sec ( 270º). If the expression is undefined, write undefined. a. undefined b. 1 c. 0 d. 1 30. Find the exact value of cot 45º. If the expression is undefined, write undefined. a. 0 b. 1 c. 1 d. undefined 31. Evaluate to the nearest hundredth. The angle is given in radians. a. 0.58 b. 0.58 c. 1.73 d. 0 Short Answer 32. Consider the graph of the cosine function shown below. a. Find the period and amplitude of the cosine function. b. At what values of for do the maximum value(s), minimum values(s), and zeros occur? 33. a. Sketch at least one cycle of a sine curve with amplitude 4 and period of 1 π. Assume a > 0. 2 b. Write an equation for the graph.

Algebra II B Review 5 Answer Section MULTIPLE CHOICE 1. ANS: C OBJ: 13-2.1 Working With Angles in Standard Position STA: MI A2.10.1 MI A2.10.3 2. ANS: C OBJ: 13-2.1 Working With Angles in Standard Position STA: MI A2.10.1 MI A2.10.3 3. ANS: B OBJ: 13-2.2 Using the Unit Circle STA: MI A2.10.1 MI A2.10.3 4. ANS: B OBJ: 13-2.2 Using the Unit Circle STA: MI A2.10.1 MI A2.10.3 5. ANS: D OBJ: 13-3.1 Using Radian Measure STA: MI A2.10.2 MI A2.10.3 6. ANS: A OBJ: 13-3.1 Using Radian Measure STA: MI A2.10.2 MI A2.10.3 7. ANS: A OBJ: 13-3.1 Using Radian Measure STA: MI A2.10.2 MI A2.10.3 8. ANS: B OBJ: 13-3.1 Using Radian Measure STA: MI A2.10.2 MI A2.10.3 9. ANS: C OBJ: 13-4.1 Interpreting Sine Functions 10. ANS: C OBJ: 13-4.1 Interpreting Sine Functions 11. ANS: A OBJ: 13-4.1 Interpreting Sine Functions 12. ANS: B OBJ: 13-4.1 Interpreting Sine Functions 13. ANS: C OBJ: 13-4.2 Graphing Sine Functions 14. ANS: A OBJ: 13-4.2 Graphing Sine Functions 15. ANS: A OBJ: 13-5.1 Graphing and Writing Cosine Functions 16. ANS: D OBJ: 13-5.2 Solving Trigonometric Equations 17. ANS: B OBJ: 13-5.2 Solving Trigonometric Equations 18. ANS: C OBJ: 13-5.2 Solving Trigonometric Equations 19. ANS: B OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1 20. ANS: C OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1 21. ANS: B OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1 22. ANS: D OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1 23. ANS: B OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1 24. ANS: C OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1 25. ANS: C OBJ: 13-5.1 Graphing and Writing Cosine Functions

26. ANS: B OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6 27. ANS: C OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6 28. ANS: D OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6 29. ANS: A OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6 30. ANS: B OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6 31. ANS: A OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6 SHORT ANSWER 32. ANS: a. The period is 1 π and the amplitude is 4. 2 1 b. maximum values: 0 : 2 π : π : 3 2 π : 2π minimum values: 1 4 π : 3 4 π : 5 4 π : 7 4 π zeros: 1 8 π : 3 8 π : 5 8 π : 7 8 π : 9 8 π : 11 8 π : 13 8 π : 15 8 π OBJ: 13-5.1 Graphing and Writing Cosine Functions 33. ANS: a. b. y = 4 sin 4θ OBJ: 13-4.2 Graphing Sine Functions

2024 © sciencedocbox.com Privacy Policy | Terms of Service | Feedback