NOTES Show all necessary work. You are not allowed to use your unit circle on the test. The test will include a non-calculator portion

Similar documents
MATH 130 FINAL REVIEW

Math Section 4.3 Unit Circle Trigonometry

Trigonometry Final Exam Review

Chapter 4 Trigonometric Functions

Section 6.2 Trigonometric Functions: Unit Circle Approach

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.

Chapter 5: Trigonometric Functions of Angles Homework Solutions

Pre-calculus Notes: Chapter 5 The Trigonometric Functions. Use the word bank below to fill in the blanks below. You may use each term only once.

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

D) sin A = D) tan A = D) cos B =

( )( ) Algebra 136 Semester 2 Review. ( ) 6. g( h( x) ( ) Name. In 1-6, use the functions below to find the solutions.

MPE Review Section II: Trigonometry

Midterm 3 Review Questions

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.

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

Find the length of an arc that subtends a central angle of 45 in a circle of radius 8 m. Round your answer to 3 decimal places.

Unit Circle. Return to. Contents

Special Angles 1 Worksheet MCR3U Jensen

download instant at

Sect 7.4 Trigonometric Functions of Any Angles

More with Angles Reference Angles

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

PART I: NO CALCULATOR (144 points)

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

Lesson 28 Working with Special Triangles

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

and sinθ = cosb =, and we know a and b are acute angles, find cos( a+ b) Trigonometry Topics Accuplacer Review revised July 2016 sin.

Pre-Calculus 40 Final Outline/Review:

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.

Lesson 16: Applications of Trig Ratios to Find Missing Angles

Math Worksheet 1 SHOW ALL OF YOUR WORK! f(x) = (x a) 2 + b. = x 2 + 6x + ( 6 2 )2 ( 6 2 )2 + 7 = (x 2 + 6x + 9) = (x + 3) 2 2

Using the Definitions of the Trigonometric Functions

1) SSS 2) SAS 3) ASA 4) AAS Never: SSA and AAA Triangles with no right angles.

Tuesday, May 2, 2006

Pre- Calculus Mathematics Trigonometric Identities and Equations

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.

Practice Problems for MTH 112 Exam 2 Prof. Townsend Fall 2013

NON-AP CALCULUS SUMMER PACKET

Find: sinθ. Name: Date:

Precalculus A - Final Exam Review Fall, 2014

Algebra II B Review 5

Mth 133 Trigonometry Review Problems for the Final Examination

8.6 Inverse Trigonometric Ratios

Ch6prac 1.Find the degree measure of the angle with the given radian measure. (Round your answer to the nearest whole number.) -2

Trigonometry LESSON SIX - Trigonometric Identities I Lesson Notes

Chapter 13: Trigonometry Unit 1

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

Lesson 33 - Trigonometric Identities. Pre-Calculus

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

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

Trigonometric Ratios. θ + k 360

Trig. Trig is also covered in Appendix C of the text. 1SOHCAHTOA. These relations were first introduced

Practice Test - Chapter 4

CK- 12 Algebra II with Trigonometry Concepts 1

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

Square Root Functions 10.1

1.1 Angles, Degrees, and Arcs

Exam Review 2 nd Semester 6-1 Operations on Functions

Name DIRECTIONS: PLEASE COMPLET E ON A SEPARATE SHEET OF PAPER. USE THE ANSWER KEY PROVIDED TO CORRECT YOUR WORK. THIS WILL BE COLLECTED!!!

Warm Up = = 9 5 3) = = ) ) 99 = ) Simplify. = = 4 6 = 2 6 3

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

Trigonometric ratios:

AP Calculus Summer Packet

Radicals and Pythagorean Theorem Date: Per:

Old Math 120 Exams. David M. McClendon. Department of Mathematics Ferris State University

Trigonometry Unit 5. Reflect previous TEST mark, Overall mark now. Looking back, what can you improve upon?

#12 Algebra 2 Notes Using Trig in Real Life

Math Section 4.3 Unit Circle Trigonometry

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

Trigonometry Math 076

Lesson 1: Trigonometry Angles and Quadrants

Solutions for Trigonometric Functions of Any Angle

Practice Questions for Midterm 2 - Math 1060Q Fall

Honors Algebra 2 Chapter 14 Page 1

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

(A) (12, 5) (B) ( 8, 15) (C) (3,6) (D) (4,4)

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

PreCalculus Second Semester Review Ch. P to Ch. 3 (1st Semester) ~ No Calculator

Section 6.2 Notes Page Trigonometric Functions; Unit Circle Approach

4-6 Inverse Trigonometric Functions

Unit 3 Right Triangle Trigonometry - Classwork

Exercise Set 4.3: Unit Circle Trigonometry

25 More Trigonometric Identities Worksheet

Chapter 3. Radian Measure and Circular Functions. Section 3.1: Radian Measure. π 1.57, 1 is the only integer value in the

Honors PreCalculus Final Exam Review Mr. Serianni

United Arab Emirates University

Lesson 22 - Trigonometric Identities

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

Chapter 5 Analytic Trigonometry

1.1 Angles and Degree Measure

Use a calculator to find the value of the expression in radian measure rounded to 2 decimal places. 1 8) cos-1 6

PRACTICE PROBLEMS CH 8 and Proofs

Unit 6: 10 3x 2. Semester 2 Final Review Name: Date: Advanced Algebra

CHAPTER 1. ANGLES AND BASIC TRIG

A2T Trig Packet Unit 1

Geometry Right Triangles and Trigonometry

n power Name: NOTES 2.5, Date: Period: Mrs. Nguyen s Initial: LESSON 2.5 MODELING VARIATION

MATH 1316 REVIEW FOR FINAL EXAM

: SINE, COSINE, & TANGENT RATIOS

Solve the equation. 1) x + 1 = 2 x. Use a method of your choice to solve the equation. 2) x2 + 3x - 28 = 0

Transcription:

Algebra Trig hapter 1 Review Problems omplete the following problems on a separate piece of paper. NOTES Show all necessary work. You are not allowed to use your unit circle on the test. The test will include a non-calculator portion 1-1 Right Triangle Trig 1. Use the triangle at right to find each of the six trigonometric functions of θ Use simplified radical form.. Find the value of x. a) b) x 100mm A θ 8 15 5 I need to use: soh cah toa x 1. When a 6-foot tall pole casts a 4-foot shadow, what is the angle of elevation of the sun? (Round the nearest degree). 1. Angles and Angle Measure 5. Draw each angle in standard position: a. 5 b. 190 c. -100 I can add or subtract 60 6. Find positive angles coterminal with each of the following: a. 400 b. -445 c. 0

1-4 Law of Sines 7. Find the area of each triangle: a. A b. =, a = 18, b = 15 54 11 14 8. Solve DA. (You may get 0, 1 or solutions!!) a. A= 50, a = 4, b = 40 b. A= 4, a =, b = 8 c. A= 15, a =, b = 15 9. Sarah Phillips, an officer for the Department of Fisheries and Wildlife, checks boaters on a lake to make sure they do not disturb two osprey nesting sites. She leaves a dock and heads due north in her boat to the first nesting site. From here, she turns 5 north of due west and travels an additional.14 miles to the second nesting site. She the travels 6.7 miles directly back to the dock. How far from the dock is the first nesting site? Round to the nearest tenth. 1-5 Law of osines 10. Solve DA. a. = 5, a = 5, b = 8 b. = 71, c = 6, a = 11 c. a = 16.4, b= 1.1, c = 18.5 11. A balloonist is directly above a straight road 1.5 miles long that joins two villages. she find that the town closer to her is at an angle of depression of 5 and the farther town is at an angle of depression of 1. How high above the ground is the balloon?

1./1.6 Trigonometric Functions of General Angles 1. Find the reference angle for each of the following a. b. -10 c. 15 1. Find the exact value of each expression. Do not use a calculator or unit circle. 1π 7π a. tan 10 b. cot (-10 ) c. csc 510 d. cos e. sec f. sin 4 6 9π cos60 + sin 0 g. cos h. csc8π i. j. (sin 0 ) + (cos0 ) 4 1.7 Inverse Trigonometric Functions 14. Find the exact value of each expression. Do not use a calculator. a. Sin -1 1 b. os -1 1 c. Tan -1 d. arccos e. tan(sin -1 1 )

h 1 Review Answers LANK WORKSHEET -PAGE DOWN omplete the following problems on a separate piece of paper. NOTES Show all necessary work. You are not allowed to use your unit circle on the test. The test will include a non-calculator portion 1-1 Right Triangle Trig 1. Use the triangle at right to find each of the six trigonometric functions of θ Use simplified radical form. 5 89 8 89 5 sinθ = cosθ = tan θ θ = 89 89 8 89 89 8 cscθ = secθ = cotθ = 5 8 5. Find the value of x. a) b) x x tan = 15 15 100 A tan x = x = 4. 5mm 100mm 1 x = 6 1 5 I need to use: soh cah toa x. When a 6-foot tall pole casts a 4-foot shadow, what is the angle of elevation of the sun? (Round the nearest degree). 6 tan x = Angles and Angle Measure 4 x = 56 5. Draw each angle in standard position: a. 5 b. 190 c. -100 I can add or subtract 60 6. Find positive angles coterminal with each of the following: a. 400 b. -445 c. 0 40 75 0

1-4 Law of Sines 7. Find the area of each triangle: a. A b. =, a = 18, b = 15 Area= 6.9un 54 11 14 Area =71.55un 8. Solve DA. (You may get 0, 1 or solutions!!) a. A= 50, a = 4, b = 40 = 64, = 66, c = 40. 5 # = 116, = 14, c = 10. 7 b. A= 4, a =, b = 8 c. A= 15, a =, b = 15 = 4, = 1, c = 9. 6 9. Sarah Phillips, an officer for the Department of Fisheries and Wildlife, checks boaters on a lake to make sure they do not disturb two osprey nesting sites. She leaves a dock and heads due north in her boat to the first nesting site. From here, she turns 5 north of due west and travels an additional.14 miles to the second nesting site. She the travels 6.7 miles directly back to the dock. How far from the dock is the first nesting site? Round to the nearest tenth. 6.14 miles 1-5 Law of osines 10. Solve DA. a. = 5, a = 5, b = 8 b. = 71, c = 6, a = 11 c. a = 16.4, b= 1.1, c = 18.5 A = 6, = 109 c = 4. 84 =, A = 77, b = 10. 67 = 58, A = 48, = 74 11. A balloonist is directly above a straight road 1.5 miles long that is between villages. She notes that the angle of depression to the village closest to her is 5 and the angle of depression to the other village is 1. How high above the ground is the balloon?.485miles

1./1.6 Trigonometric Functions of General Angles 1. Find the reference angle for each of the following a. b. -10 c. 15 π 60 45 1. Find the exact value of each expression. Do not use a calculator or unit circle. 1π 7π a. tan 10 b. cot (-10 ) c. csc 510 d. cos e. sec f. sin 4 6 9π g. cos h. csc8π i. cos60 + sin 0 4 1 0 undefined 1 4 j. (sin 0 ) + (cos0 ) 1.7 Inverse Trigonometric Functions 14. Find the exact value of each expression. Do not use a calculator. a. Sin -1 1 b. os -1 1 c. Tan -1 d. arccos 90 60 0 15 e. tan(sin -1 1 )