Name c V2M0W1H7O MKwuYtxaa ]SooUfBt[wEaxrYed alxlkcb.a K NAMlFlH qrniig\hltosf Fr`eVsJeSryvze_dX. -1-

Similar documents
5, tan = 4. csc = Simplify: 3. Simplify: 4. Factor and simplify: cos x sin x cos x

Math 370 Exam 3 Review Name

Math 370 Exam 3 Review Name

Exercise Set 4.3: Unit Circle Trigonometry

MTH 122: Section 204. Plane Trigonometry. Test 1

( ) + ( ) ( ) ( ) Exercise Set 6.1: Sum and Difference Formulas. β =, π π. π π. β =, evaluate tan β. Simplify each of the following expressions.

Chapter 4 Trigonometric Functions

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

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

Honors PreCalculus Final Exam Review Mr. Serianni

Trigonometric Identities Exam Questions

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

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

Unit 2 - The Trigonometric Functions - Classwork

7.1 Right Triangle Trigonometry; Applications Objectives

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

Trigonometric Functions. Section 1.6

12.1 Three Dimensional Coordinate Systems (Review) Equation of a sphere

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

Math Section 4.3 Unit Circle Trigonometry

Math 2412 Pre Calculus TEST 2 Prep Fall 2011

4-3 Trigonometric Functions on the Unit Circle

2.1 Limits, Rates of Change and Slopes of Tangent Lines

Precalculus A - Final Exam Review Fall, 2014

Honors Pre-Calculus Summer Work

University Calculus I. Worksheet # 8 Mar b. sin tan e. sin 2 sin 1 5. b. tan. c. sec sin 1 ( x )) cos 1 ( x )) f. csc. c.

Practice Test - Chapter 4

2. Pythagorean Theorem:

9.1 VECTORS. A Geometric View of Vectors LEARNING OBJECTIVES. = a, b

PreCalculus Second Semester Review Chapters P-3(1st Semester)

Trigonometry LESSON SIX - Trigonometric Identities I Lesson Notes

CHAPTER 5: Analytic Trigonometry

Practice Test - Chapter 4

Chapter 6 Additional Topics in Trigonometry, Part II

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

Fundamental Trigonometric Identities

The Other Trigonometric

Exam Review 2 nd Semester 6-1 Operations on Functions

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

Trigonometric Functions. Copyright Cengage Learning. All rights reserved.

PART 1: USING SCIENTIFIC CALCULATORS (50 PTS.)

Math Section 4.3 Unit Circle Trigonometry

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

Math 8 Winter 2010 Midterm 2 Review Problems Solutions - 1. xcos 6xdx = 4. = x2 4

Section 6.2 Notes Page Trigonometric Functions; Unit Circle Approach

Milford Public Schools Curriculum. Department: Mathematics Course Name: Precalculus Level 1

Problems with an # after the number are the only ones that a calculator is required for in the solving process.

Pre Calc. Trigonometry.

Math 102 Spring 2008: Solutions: HW #3 Instructor: Fei Xu

Chapter 5: Double-Angle and Half-Angle Identities

Lesson 7.3 Exercises, pages

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

Precalculus Midterm Review

Notes on Radian Measure

Course Learning Objectives: Demonstrate an understanding of trigonometric functions and their applications.

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

Transition to College Math

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

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

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 :

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 :

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

Exercise Set 4.1: Special Right Triangles and Trigonometric Ratios

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

MATH 109 TOPIC 3 RIGHT TRIANGLE TRIGONOMETRY. 3a. Right Triangle Definitions of the Trigonometric Functions

9.1 VECTORS. A Geometric View of Vectors LEARNING OBJECTIVES. = a, b

Summer Assignment MAT 414: Calculus

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

6.2 Trigonometric Integrals and Substitutions

Pre-Calc Trigonometry

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

Unit Circle. Return to. Contents

PART A: Solve the following equations/inequalities. Give all solutions. x 3 > x + 3 x

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

CK- 12 Algebra II with Trigonometry Concepts 1

1 The six trigonometric functions

Pre-Calculus Exam 2009 University of Houston Math Contest. Name: School: There is no penalty for guessing.

Chapter 1. Functions 1.3. Trigonometric Functions

Problems with an # after the number are the only ones that a calculator is required for in the solving process.

Section 6.2 Trigonometric Functions: Unit Circle Approach

Math 2 Trigonometry. People often use the acronym SOHCAHTOA to help remember which is which. In the triangle below: = 15

Using the Definitions of the Trigonometric Functions

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

1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.

The Other Trigonometric Functions

Ê 7, 45 Ê 7 Ë 7 Ë. Time: 100 minutes. Name: Class: Date:

MA Spring 2013 Lecture Topics

Trig Identities, Solving Trig Equations Answer Section

Math Precalculus Blueprint Assessed Quarter 1

Lesson 25 Solving Linear Trigonometric Equations

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

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

Summer Assignment for AP Calculus AB

Unit 5 PreCalculus Review

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

b) The trend is for the average slope at x = 1 to decrease. The slope at x = 1 is 1.

in Trigonometry Name Section 6.1 Law of Sines Important Vocabulary

Math 121: Calculus 1 - Fall 2013/2014 Review of Precalculus Concepts

4.3 TRIGONOMETRY EXTENDED: THE CIRCULAR FUNCTIONS

Transcription:

Precalculus Name c VM0W1H7O MKwuYtxaa ]SooUfBt[wEaxrYed alxlkcb.a K NAMlFlH qrniig\hltosf Fr`eVsJeSryvze_dX. Vectors Test Review Find the exact value of each trigonometric function. 1) cos 15 ) cos 10 Date Period ) tan 10 4) tan 60 5) tan 15 6) sin -405 7) cos -70 8) sin -660 Use the given point on the terminal side of angle q to find the value of the trigonometric function indicated. 9) cos q ; (-9, 19) Find the exact values of the two trigonometric ratios not given. 10) tan q = - 0 and cos q > 0 1 t WS0a1z7o dkhuntka^ ^SXoBfgtTwQa\rNeG QLPLbCA.Z f KAZlGlz xrkipgphxtjsv ArGeKs\eersvkejd`.N n gmcapddes ]wfi^trhq liqnzfiiunsi_teeu npvrienceasldczunlbussc. -1-

Find the component form of the resultant vector. 11) Given: A = (-10, -6) B = (4, 9) C = (1, 5) D = (-5, 9) Find: -AB - CD Express the resultant vector as a linear combination of unit vectors i and j. 1) Given: A = (-5, 1) B = (6, ) C = (7, -9) D = (-10, 0) Find: AB - CD Find the component form of the resultant vector. 1) a = -1, - g = 8, 1 Find: -4a + 8g Express the resultant vector as a linear combination of unit vectors i and j. 14) u = i - j g = 4i + 7j Find: 6u - 5g 15) Given: P = (-, 10) Q = (-1, -) Find the vector opposite PQ 16) Given: A = (-, -10) B = (8, -9) Find: 10AB Draw a diagram to illustrate the horizontal and vertical components of the vector. Then find the magnitude of each component. 17) m = 0, 16 d pk0l1z7n BKKuUt[aQ ZS^oSfUtTwlaorbeB FLlLBC[.z e raqlald Lrji\gjhBtOsu `rrefsyewrnvcetdr.t _ PMPa`dDex AwgiXtYhN QIrnCfpihnriwtMed MPErHekc[a_lucIuClbutsz. --

Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. Then state the magnitude and direction angle of the resultant. 18) t = 16, 10 u = 1, -16 19) t = -15, 5 u = 9, -1 Find the following information for each vector, if not provided in the question: Linear combination, magnitude and direction angle. 0) v = -9, 16 1) k = 50, 1 Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. Then state the magnitude and direction angle of the resultant. ) t = -8, 15 u = 18, 14 F _I0Y1k7f `KuuetNa\ qscoufitzwxaprhem OL\LNCh.O I GAclUly HrZivgChMtRsF FrEeisOeGrWvdemdI.U U nmuagdle^ qwfiqtshp uicnbfgivnyi[tieu spyrzefcraclmcpuslmu^sl. --

) m = -8, -15 n = 7, Find the dot product of the given vectors. 4) u = -5, -1 v = -1, -9 Find the measure of the angle between the two vectors. 5) u = -i + 5j v = 9i - 8j 6) u = -, 7 v = 9, 8 State if the two vectors are parallel, orthogonal, or neither. 7) u = 1i - 15j v = -5i - 7j 8) u = -7, -1 v = -8, -4 D ]G0b1f7I rkcustqaj `SEoffctMwyairoec [LsLxC`.y K DAWlVlS XrLihgqhJtisG WrGe_sneArevDetdm.q a CMHaDdUeB gwdittshz ei\noftinniiptdev ZP[r\eJcHaclFcquNlRuFsP. -4-

Precalculus Name X px0y1h7a HKmuht\ad gsoowfgtpw[ayraej klplqcz.a K AAplIli NrKirguhYtMsd graeusdehrxveeudk. Vectors Test Review Find the exact value of each trigonometric function. Date Period 1) cos 15 ) cos 10 - ) tan 10 4) tan 60 5) tan 15-1 6) sin -405-7) cos -70 0 8) sin -660 Use the given point on the terminal side of angle q to find the value of the trigonometric function indicated. 9) cos q ; (-9, 19) - 9 10 Find the exact values of the two trigonometric ratios not given. 10) tan q = - 0 and cos q > 0 1 sin q = - 0 9 1 0, cos q =, tan q = - 9 1 csc q = - 9 9, sec q = 0 1 ` tp0i1z7t CKVuvttaI NSRoTfSt[w]aSrBeK dlilhcz.w a EAPlflv NrDigg[hStHsN frsedsxe_rhvieqdr.^ G PMHaBdMeh ]wtiktghe CIxnffviunYidtlem UPYrwesceaPlKcjuIlouisB. -1-

Find the component form of the resultant vector. 11) Given: A = (-10, -6) B = (4, 9) C = (1, 5) D = (-5, 9) Find: -AB - CD -8, -19 Express the resultant vector as a linear combination of unit vectors i and j. 1) Given: A = (-5, 1) B = (6, ) C = (7, -9) D = (-10, 0) Find: AB - CD 8i - 8j Find the component form of the resultant vector. 1) a = -1, - g = 8, 1 Find: -4a + 8g 68, 108 Express the resultant vector as a linear combination of unit vectors i and j. 14) u = i - j g = 4i + 7j Find: 6u - 5g -8i - 5j 15) Given: P = (-, 10) Q = (-1, -) Find the vector opposite PQ -i + 1j 16) Given: A = (-, -10) B = (8, -9) Find: 10AB 110i + 10j Draw a diagram to illustrate the horizontal and vertical components of the vector. Then find the magnitude of each component. 17) m = 0, 16 x m y Horizontal: 1.58 Vertical: -0.84 B lh0x1b7z AKXudtFa_ JSOorfktrwOaOrueU dljlyc`.w ] SAZlvlw JrZimgYhStFsy arsevsqecr`v]eudo.n X gm]atd\e` xwdiqtwhf [IHn^f\ianwiMtler XPqrSePcxaVlvcZuhluuHs\. --

Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. Then state the magnitude and direction angle of the resultant. 18) t = 16, 10 u = 1, -16 19) t = -15, 5 u = 9, -1 t u u t t + u 8.64; 47.91 9.; 9.4 t + u Find the following information for each vector, if not provided in the question: Linear combination, magnitude and direction angle. 0) v = -9, 16-9i + 16j 1097».11 151.11 1) k = 50, 1-41.94i - 7.j Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. Then state the magnitude and direction angle of the resultant. ) t = -8, 15 u = 18, 14 u t + u t 0.68; 70.97 I IO0E1h7B skkuvtdan PS\osf]tFwbanr]eV ZLFL\Cn.n J daelcle oreiogbhutbsp wraeisyeyrnvbezdw.n L QMcacdaef ewsiqtbhb GIJnSf\iZnSiltMes _PwrTe\cWaGlNcquzlOu]s^. --

) m = -8, -15 n = 7, m m + n n 1.04; 65.4 Find the dot product of the given vectors. 4) u = -5, -1 v = -1, -9 14 Find the measure of the angle between the two vectors. 5) u = -i + 5j v = 9i - 8j 16.6 6) u = -, 7 v = 9, 8 71.57 State if the two vectors are parallel, orthogonal, or neither. 7) u = 1i - 15j v = -5i - 7j Orthogonal 8) u = -7, -1 v = -8, -4 Parallel h w\0w1v7g dkiu_tlai ysnotfzthwbamrse` plul\cn.t b VAulGl\ prfilgihpt]sq arwevslevrjvqewdl.n Z nmmacduew jwiigtchw UIenYfyiLnbiztSel JPfr`eWcua\l\cZuQlfuzsp. -4-