MATH 1112 FINAL EXAM REVIEW e. None of these. d. 1 e. None of these. d. 1 e. None of these. e. None of these. e. None of these.
|
|
- Jeffry Dorsey
- 5 years ago
- Views:
Transcription
1 I. State the equation of the unit circle. MATH 111 FINAL EXAM REVIEW x y y = 1 x+ y = 1 x = 1 x + y = 1 II. III. If 1 tan x =, find sin x for x in Quadrant IV Give the exact value of each expression sin 1 0 Undefined. cos Undefined 1. sin10. cos
2 . cos 6. cos Undefined 7. tan 1 8. cot Undefined 9. sec csc0 Undefined 0 1 IV. Which of the following is a sketch of the graph of the given function on [0, )? 1. y = sin x
3 . y = cos x. y = tan x
4 . y = cot x. y = sec x
5 6. y = csc x
6 V. Simplify each expression. 1. cos( θ ) cosθ cosθ sinθ sinθ. sin( θ ) cosθ cosθ sinθ sinθ. tan( θ ) tanθ tanθ cotθ cotθ. sec( θ ) secθ secθ cscθ cscθ VI. Evaluate each expression. 1. arccos 7. 1 sin
7 . 1 csccot 1. tan ( 1) 7 6 VII. Which of the following is a sketch of one cycle of the graph of each function? 1. y = sin x. y ( x ) = cos + +
8 . y = tan x
9 . y = cot ( x+ ). y = sec x
10 6. y = csc( x ) 1
11 VIII. Use the sum or difference identities to evaluate each expression. 1. cos sin e. None of these. tan IX. Let α be in Quadrant I, β in Quadrant III, 7 cosα =, and tan β = ( α β) cos =? ( α β) sin + =? 0. ( α β) tan + =?
12 6 X. Change each sum or difference to a product. 1. sin 68 + sin cos0 cos18 sin 0 sin18 cos0 sin18 sin 0 cos18. sin x sin x cos xsin x sin x cos8x sin x cos xsin x. cos1x+ cos x cos17x 17x 7x sin sin 17x 7x sin cos 17x 7x cos cos. cos 0 cos 0 sin10 sin10 cos 0 cos10 XI. Let θ be in Quadrant II with 1 secθ =. 1. sin θ =? e. None of these 1
13 . cos θ =? 1. tan θ =? XII. Evaluate each of the following expressions using the half-angle identities. 1. sin cos tan XIII. If the terminal side of θ passes through the point (-,), find sin θ XIV. Solve each equation for 0 x <. 1. cos x= 1 sin x 1 1
14 7 11 0,,, 0,,, 0,,, , sin xcos x=,,,,. cos sin 1 0 x+ x =,, 6 6,, 6 6,, 7 11,, 6 6. cot x 1 = ,,,,,,, ,,, ,,, ,,,,,,, XV. Solve ABC for the missing part. 1. A= 90, a = 9, b= 1, B=? a =, b= 8, c= 10, C =?
15 . A= 0, b= 6, B= 0, c=? XVI. Give the radian measure of an angle that subtends an arc of length in a circle of radius None of these. XVII. Convert to degrees XVIII. Convert 60 to radians XIX. Simplify each expression. 1. sinθsecθ cotθ 1 sin θ tanθ. cos θ tan θ + cos θ 1 cot θ cos θ tan θ sin θ e. None of these. cscθ + secθ sinθ + cosθ 1 sinθ + cosθ csc θ + sec θ cscθsecθ
16 . ( ) sin x+ cos x sin x 1 1+ sin x sin xcos x. sec sec x tan x+ tan x x tan x 1 sec x tan x sin θ cotθ cos θsinθ cotθ secθ cosθsinθ cotθ XX. Change the product to a sum. 1. 6sin1 sin + +. sin xcos x cosx+ cos x sin x+ sin x cosx cos x cos x+ cos x. cos 8 sin 0 sin 68 sin1 1 1 sin 68 sin1 1 1 sin 68 + sin1 cos 68 + cos1
17 . cos 7xcosx 1 1 cos1x+ cos x 1 1 sin1x+ sin x 1 1 cos1x cos x 1 1 sin1x sin x XXI. Let the point 1, be a point on the terminal side of an angle θ in standard position. Find the sine and cosine of θ. 1 cos θ = ;sinθ = 1 sin θ = ;cosθ = 1 cos θ = ;sinθ = cosθ = ;sin θ = 1 1 XXII. For each of the following, give the quadrant in which the terminal ray of θ lies. 1. tanθ < 0 and cosθ > 0 I II III IV. cscθ > 0 and cot θ<0 I II III IV XXIII. Give the reference angle for the indicated angle
18 XXIV.Find the quadrant in which the indicated angle lies I II III IV I II III IV.. I II III IV. 1 I II III IV
19 XXV. Which of the following angles are coterminal with the given angle? XXVI.Give the amplitude of the function f ( x) = 7 cos x XXVII.Give the period of the function f ( x) = 8sin 9 x XXVIII.Give the period of the function f ( x) = tan x XXIX.Given the following data set for ABC, how many triangles can be drawn?
20 1. a = 1, b= 0, A= 1 0. a = 8, b= 1, A= 1 0 XXX. If cosθ =, θ in Quadrant III, find the value of tanθ XXXI. The length of an arc of the unit circle is as given. Name the quadrant within which the terminal point would lie. 1. t = I II III IV.. 1 t = 1 I II III IV.. t = 0 9 I II III IV.
21 . t =.78 I II III IV. XXXII.Give the terminal point on the unit circle for an arc of the length below. 1. t = 7 6 1, 1, 1, 1, None of these.. t =,,, ( 0, 1) None of these.. t = 1, 1, 1, 1, XXXIV.Complete the following statements: 1. 1 sin θ = tan θ sinθ cosθ
22 cos θ. sec θ tan θ = secθ tanθ sinθ 1 cos θ. = cos 7x sin 7 x 1 sin1x cos1x 0. 1 cos 0 = cos sin sin100 cos cot 9 x = csc 9x cot 10x sec 9x cos 9x 6. cos ( θ ) + = cosθ sinθ sinθ cosθ 7. ( θ ) sin + = cosθ sinθ sinθ cosθ
23 ANSWERS: I. c II. d III. 1. d. a. c. c. a 6. a 7. b 8. d 9. d 10. a IV. 1. b. a. a. b. b 6. a V. 1. b. d. a. b VI. 1. d. c. d. b VII. 1. d. c. c. a. a 6. a VIII. 1. d. c. a IX. 1. b. c. d X. 1. d. d. d. a XI. 1.. d. a XII. 1. b. c. c XIII. b XIV. 1. a. d. c. a XV. 1. b. b. a XVI. b XVII. a XVIII. b XIX. 1. d. a. d. c. d 6. c XX. 1. a. b XXI. a XXII. d XXIII. 1. c. d. a XXIV.1. b. a. d. b XXV. 1. b. a XXVI. b XXVII. d XXVIII. b XXIX. 1. b. d
Math 104 Final Exam Review
Math 04 Final Exam Review. Find all six trigonometric functions of θ if (, 7) is on the terminal side of θ.. Find cosθ and sinθ if the terminal side of θ lies along the line y = x in quadrant IV.. Find
More information6.4 & 6.5 Graphing Trigonometric Functions. The smallest number p with the above property is called the period of the function.
Math 160 www.timetodare.com Periods of trigonometric functions Definition A function y f ( t) f ( t p) f ( t) 6.4 & 6.5 Graphing Trigonometric Functions = is periodic if there is a positive number p such
More informationPythagorean Identity. Sum and Difference Identities. Double Angle Identities. Law of Sines. Law of Cosines
Review for Math 111 Final Exam The final exam is worth 30% (150/500 points). It consists of 26 multiple choice questions, 4 graph matching questions, and 4 short answer questions. Partial credit will be
More informationSection 8.1 Radians and Arc Length
Section 8. Radians and Arc Length Definition. An angle of radian is defined to be the angle, in the counterclockwise direction, at the center of a unit circle which spans an arc of length. Conversion Factors:
More informationMHF4U. Advanced Functions Grade 12 University Mitchell District High School. Unit 4 Radian Measure 5 Video Lessons
MHF4U Advanced Functions Grade 12 University Mitchell District High School Unit 4 Radian Measure 5 Video Lessons Allow no more than 1 class days for this unit! This includes time for review and to write
More information2. (8pts) If θ is an acute angle, find the values of all the trigonometric functions of θ given
Trigonometry Joysheet 1 MAT 145, Spring 2017 D. Ivanšić Name: Covers: 6.1, 6.2 Show all your work! 1. 8pts) If θ is an acute angle, find the values of all the trigonometric functions of θ given that sin
More informationRevised Curriculum for Bachelor of Computer Science & Engineering, 2011
Revised Curriculum for Bachelor of Computer Science & Engineering, 2011 FIRST YEAR FIRST SEMESTER al I Hum/ T / 111A Humanities 4 100 3 II Ph /CSE/T/ 112A Physics - I III Math /CSE/ T/ Mathematics - I
More informationMAC 1114 REVIEW FOR EXAM #2 Chapters 3 & 4
MAC 111 REVIEW FOR EXAM # Chapters & This review is intended to aid you in studying for the exam. This should not be the only thing that you do to prepare. Be sure to also look over your notes, textbook,
More informationRethinking the Licensing of New Attorneys - An Exploration of Alternatives to the Bar Exam: Introduction
Georgia State University Law Review Volume 20 Issue 4 Summer 2004 Article 3 9-1-2003 Rethinking the Licensing of New Attorneys - An Exploration of Alternatives to the Bar Exam: Introduction Clark D. Cunningham
More informationPreCalc: Chapter 6 Test Review
Name: Class: Date: ID: A PreCalc: Chapter 6 Test Review Short Answer 1. Draw the angle. 135 2. Draw the angle. 3. Convert the angle to a decimal in degrees. Round the answer to two decimal places. 8. If
More informationDouble-Angle, Half-Angle, and Reduction Formulas
Double-Angle, Half-Angle, and Reduction Formulas By: OpenStaxCollege Bicycle ramps for advanced riders have a steeper incline than those designed for novices. Bicycle ramps made for competition (see [link])
More informationArkansas Tech University MATH 1203: Trigonometry Dr. Marcel B. Finan. Review Problems for Test #3
Arkansas Tech University MATH 1203: Trigonometry Dr. Marcel B. Finan Review Problems for Test #3 Exercise 1 The following is one cycle of a trigonometric function. Find an equation of this graph. Exercise
More informationθ = = 45 What is the measure of this reference angle?
OF GENERAL ANGLES Our method of using right triangles only works for acute angles. Now we will see how we can find the trig function values of any angle. To do this we'll place angles on a rectangular
More informationMATH 1040 CP 15 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
MATH 1040 CP 15 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) (sin x + cos x) 1 + sin x cos x =? 1) ) sec 4 x + sec x tan x - tan 4 x =? ) ) cos
More informationSolutions to Exercises, Section 5.6
Instructor s Solutions Manual, Section 5.6 Exercise 1 Solutions to Exercises, Section 5.6 1. For θ = 7, evaluate each of the following: (a) cos 2 θ (b) cos(θ 2 ) [Exercises 1 and 2 emphasize that cos 2
More informationFerris Wheel Activity. Student Instructions:
Ferris Wheel Activity Student Instructions: Today we are going to start our unit on trigonometry with a Ferris wheel activity. This Ferris wheel will be used throughout the unit. Be sure to hold on to
More informationMath 1205 Trigonometry Review
Math 105 Trigonometry Review We begin with the unit circle. The definition of a unit circle is: x + y =1 where the center is (0, 0) and the radius is 1. An angle of 1 radian is an angle at the center of
More informationUnit 5. Algebra 2. Name:
Unit 5 Algebra 2 Name: 12.1 Day 1: Trigonometric Functions in Right Triangles Vocabulary, Main Topics, and Questions Definitions, Diagrams and Examples Theta Opposite Side of an Angle Adjacent Side of
More informationUnit 6 Test REVIEW Algebra 2 Honors
Unit Test REVIEW Algebra 2 Honors Multiple Choice Portion SHOW ALL WORK! 1. How many radians are in 1800? 10 10π Name: Per: 180 180π 2. On the unit circle shown, which radian measure is located at ( 2,
More information= tanθ 3) cos2 θ. = tan θ. = 3cosθ 6) sinθ + cosθcotθ = cscθ. = 3cosθ. = 3cosθ sinθ
PRE-CALCULUS/TRIGONOMETRY 3 Name 5.-5.5 REVIEW Date: Block Verify. ) cscθ secθ = cotθ 2) sec2 θ tanθ = tanθ 3) cos2 θ +sin θ = Use RIs sin θ = cotθ tan 2 θ tanθ = tan θ sin 2 θ +sin θ = Multiply by reciprocal
More informationMath Section 4.3 Unit Circle Trigonometry
Math 0 - Section 4. Unit Circle Trigonometr An angle is in standard position if its verte is at the origin and its initial side is along the positive ais. Positive angles are measured counterclockwise
More informationMod E - Trigonometry. Wednesday, July 27, M132-Blank NotesMOM Page 1
M132-Blank NotesMOM Page 1 Mod E - Trigonometry Wednesday, July 27, 2016 12:13 PM E.0. Circles E.1. Angles E.2. Right Triangle Trigonometry E.3. Points on Circles Using Sine and Cosine E.4. The Other Trigonometric
More informationAPPLICATION FOR APPROVAL OF A IENG EMPLOYER-MANAGED FURTHER LEARNING PROGRAMME
APPLICATION FOR APPROVAL OF A IENG EMPLOYER-MANAGED FURTHER LEARNING PROGRAMME When completing this application form, please refer to the relevant JBM guidance notably those setting out the requirements
More informationMathematics Lecture. 3 Chapter. 1 Trigonometric Functions. By Dr. Mohammed Ramidh
Mathematics Lecture. 3 Chapter. 1 Trigonometric Functions By Dr. Mohammed Ramidh Trigonometric Functions This section reviews the basic trigonometric functions. Trigonometric functions are important because
More informationWhyTry Elementary Game Plan Journal
WhyTry Elementary Game Plan Journal I can promise you that if you will do the things in this journal, develop a Game Plan for your life, and stick to it, you will get opportunity, freedom, and self respect;
More informationMathematics UNIT FIVE Trigonometry II. Unit. Student Workbook. Lesson 1: Trigonometric Equations Approximate Completion Time: 4 Days
Mathematics 0- Student Workbook Unit 5 Lesson : Trigonometric Equations Approximate Completion Time: 4 Days Lesson : Trigonometric Identities I Approximate Completion Time: 4 Days Lesson : Trigonometric
More informationTrig/AP Calc A. Created by James Feng. Semester 1 Version fengerprints.weebly.com
Trig/AP Calc A Semester Version 0.. Created by James Feng fengerprints.weebly.com Trig/AP Calc A - Semester Handy-dandy Identities Know these like the back of your hand. "But I don't know the back of my
More information4-3 Trigonometric Functions on the Unit Circle
Find the exact values of the five remaining trigonometric functions of θ. 33. tan θ = 2, where sin θ > 0 and cos θ > 0 To find the other function values, you must find the coordinates of a point on the
More informationSection 5.1 Angles and Radian Measure. Ever Feel Like You re Just Going in Circles?
Section 5.1 Angles and Radian Measure Ever Feel Like You re Just Going in Circles? You re riding on a Ferris wheel and wonder how fast you are traveling. Before you got on the ride, the operator told you
More information2. Be able to evaluate a trig function at a particular degree measure. Example: cos. again, just use the unit circle!
Study Guide for PART II of the Fall 18 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 be
More informationPREREQUISITE/PRE-CALCULUS REVIEW
PREREQUISITE/PRE-CALCULUS REVIEW Introduction This review sheet is a summary of most of the main topics that you should already be familiar with from your pre-calculus and trigonometry course(s), and which
More informationName Date Class. Identify whether each function is periodic. If the function is periodic, give the period
Name Date Class 14-1 Practice A Graphs of Sine and Cosine Identify whether each function is periodic. If the function is periodic, give the period. 1.. Use f(x) = sinx or g(x) = cosx as a guide. Identify
More informationPre-Calc Chapter 4 Sample Test. 1. Determine the quadrant in which the angle lies. (The angle measure is given in radians.) π
Pre-Calc Chapter Sample Test 1. Determine the quadrant in which the angle lies. (The angle measure is given in radians.) π 8 I B) II C) III D) IV E) The angle lies on a coordinate axis.. Sketch the angle
More informationName:... Date:... Use your mathematical skills to solve the following problems. Remember to show all of your workings and check your answers.
Name:... Date:... Use your mathematical skills to solve the following problems. Remember to show all of your workings and check your answers. There has been a zombie virus outbreak in your school! The
More information13.4 Chapter 13: Trigonometric Ratios and Functions. Section 13.4
13.4 Chapter 13: Trigonometric Ratios and Functions Section 13.4 1 13.4 Chapter 13: Trigonometric Ratios and Functions Section 13.4 2 Key Concept Section 13.4 3 Key Concept Section 13.4 4 Key Concept Section
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 informationSection 2.7 Proving Trigonometric Identities
Sec. 2.7 Proving Trigonometric Identities 87 Section 2.7 Proving Trigonometric Identities In this section, we use the identities presented in Section 2.6 to do two different tasks: ) to simplify a trigonometric
More informationUnit 8 Trigonometry. Math III Mrs. Valentine
Unit 8 Trigonometry Math III Mrs. Valentine 8A.1 Angles and Periodic Data * Identifying Cycles and Periods * A periodic function is a function that repeats a pattern of y- values (outputs) at regular intervals.
More informationMath Problem Set 5. Name: Neal Nelson. Show Scored View #1 Points possible: 1. Total attempts: 2
Math Problem Set 5 Show Scored View #1 Points possible: 1. Total attempts: (a) The angle between 0 and 60 that is coterminal with the 69 angle is degrees. (b) The angle between 0 and 60 that is coterminal
More informationYear 10 Term 1 Homework
Yimin Math Centre Year 10 Term 1 Homework Student Name: Grade: Date: Score: Table of contents 6 Year 10 Term 1 Week 6 Homework 1 6.1 Triangle trigonometry................................... 1 6.1.1 The
More informationBasic Trigonometry You Should Know (Not only for this class but also for calculus)
Angle measurement: degrees and radians. Basic Trigonometry You Should Know (Not only for this class but also for calculus) There are 360 degrees in a full circle. If the circle has radius 1, then the circumference
More informationPrecalculus Second Semester Final Review
Precalculus Second Semester Final Review This packet will prepare you for your second semester final exam. You will find a formula sheet on the back page; these are the same formulas you will receive for
More informationHONORS PRECALCULUS Prove the following identities- ( ) x x x x x x. cos x cos x cos x cos x 1 sin x cos x 1 sin x
HONORS PRECALCULUS Prove the following identities-.) ( ) cos sin cos cos sin + sin sin + cos sin cos sin cos.).) ( ) ( sin) ( ) ( ) sin sin + + sin sin tan + sec + cos cos cos cos sin cos sin cos cos cos
More informationMath 102 Key Ideas. 1 Chapter 1: Triangle Trigonometry. 1. Consider the following right triangle: c b
Math 10 Key Ideas 1 Chapter 1: Triangle Trigonometry 1. Consider the following right triangle: A c b B θ C a sin θ = b length of side opposite angle θ = c length of hypotenuse cosθ = a length of side adjacent
More informationClass 10 Trigonometry
ID : in-10-trigonometry [1] Class 10 Trigonometry For more such worksheets visit www.edugain.com Answer t he quest ions (1) An equilateral triangle width side of length 18 3 cm is inscribed in a circle.
More informationPythagorean Theorem: Trigonometry Packet #1 S O H C A H T O A. Examples Evaluate the six trig functions of the angle θ. 1.) 2.)
Trigonometry Packet #1 opposite side hypotenuse Name: Objectives: Students will be able to solve triangles using trig ratios and find trig ratios of a given angle. S O H C A H T O A adjacent side θ Right
More informationMath 180 Chapter 6 Lecture Notes. Professor Miguel Ornelas
Math 180 Chapter 6 Lecture Notes Professor Miguel Ornelas 1 M. Ornelas Math 180 Lecture Notes Section 6.1 Section 6.1 Verifying Trigonometric Identities Verify the identity. a. sin x + cos x cot x = csc
More information1. Measure angle in degrees and radians 2. Find coterminal angles 3. Determine the arc length of a circle
Pre- Calculus Mathematics 12 5.1 Trigonometric Functions Goal: 1. Measure angle in degrees and radians 2. Find coterminal angles 3. Determine the arc length of a circle Measuring Angles: Angles in Standard
More informationI Write the Number Names 223-89 - 605-1000 - 812-437 - 893-910 - II 115-844 - Fill in the blanks 6 X 7 = 2 X 9 = 7 X 8 = 7 X 5 = 3 X10 = 6 X 7 = 5 X 5 = 3 X 6 = 6 X 3 = 7 X 7 = 3 X 9 = 5 X 8 = III Write
More informationAlgebra 2/Trig AIIT.13 AIIT.15 AIIT.16 Reference Angles/Unit Circle Notes. Name: Date: Block:
Algebra 2/Trig AIIT.13 AIIT.15 AIIT.16 Reference Angles/Unit Circle Notes Mrs. Grieser Name: Date: Block: Trig Functions in a Circle Circle with radius r, centered around origin (x 2 + y 2 = r 2 ) Drop
More informationTABLEAU DES MODIFICATIONS
TABLEAU DES MODIFICATIONS APPORTÉES AUX STATUTS REFONDUS, 1964 ET AUX LOIS PUBLIQUES POSTÉRIEURES DANS CE TABLEAU Ab. = Abrogé Ann. = Annexe c. = Chapitre cc. = Chapitres Form. = Formule R. = Statuts refondus,
More informationθ = radians; where s = arc length, r = radius
TRIGONOMETRY: 2.1 Degrees & Radians Definitins: 1 degree - 1 radian θ r s FORMULA: s θ = radians; where s = arc length, r = radius r IMPLICATION OF FORMULA: If s = r then θ = 1 radian EXAMPLE 1: What is
More informationTrigonometric identities
Trigonometric identities An identity is an equation that is satisfied by all the values of the variable(s) in the equation. For example, the equation (1 + x) = 1 + x + x is an identity. If you replace
More informationMATH 130 FINAL REVIEW version2
MATH 130 FINAL REVIEW version2 Problems 1 3 refer to triangle ABC, with =. Find the remaining angle(s) and side(s). 1. =50, =25 a) =40,=32.6,=21.0 b) =50,=21.0,=32.6 c) =40,=21.0,=32.6 d) =50,=32.6,=21.0
More informationTrigonometry. David R. Wilkins
Trigonometry David R. Wilkins 1. Trigonometry 1. Trigonometry 1.1. Trigonometric Functions There are six standard trigonometric functions. They are the sine function (sin), the cosine function (cos), the
More informationTrigonometric Identities. Copyright 2017, 2013, 2009 Pearson Education, Inc.
5 Trigonometric Identities Copyright 2017, 2013, 2009 Pearson Education, Inc. 1 5.3 Sum and Difference Identities Difference Identity for Cosine Sum Identity for Cosine Cofunction Identities Applications
More informationSECTION 1.5: TRIGONOMETRIC FUNCTIONS
SECTION.5: TRIGONOMETRIC FUNCTIONS The Unit Circle The unit circle is the set of all points in the xy-plane for which x + y =. Def: A radian is a unit for measuring angles other than degrees and is measured
More informationGeometry Problem Solving Drill 11: Right Triangle
Geometry Problem Solving Drill 11: Right Triangle Question No. 1 of 10 Which of the following points lies on the unit circle? Question #01 A. (1/2, 1/2) B. (1/2, 2/2) C. ( 2/2, 2/2) D. ( 2/2, 3/2) The
More informationAlgebra2/Trig Chapter 10 Packet
Algebra2/Trig Chapter 10 Packet In this unit, students will be able to: Convert angle measures from degrees to radians and radians to degrees. Find the measure of an angle given the lengths of the intercepted
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Trigonometry Final Exam Study Guide Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a polar equation is given. Select the polar
More informationChapter 1 and Section 2.1
Chapter 1 and Section 2.1 Diana Pell Section 1.1: Angles, Degrees, and Special Triangles Angles Degree Measure Angles that measure 90 are called right angles. Angles that measure between 0 and 90 are called
More information3.2 Proving Identities
3.. Proving Identities www.ck.org 3. Proving Identities Learning Objectives Prove identities using several techniques. Working with Trigonometric Identities During the course, you will see complex trigonometric
More informationTriangle Definition of sin θ and cos θ
Triangle Definition of sin θ and cos θ Then Consider the triangle ABC below. Let A be called θ. A HYP (hpotenuse) θ ADJ (side adjacent to the angle θ ) B C OPP (side opposite to the angle θ ) (SOH CAH
More informationChapter 1. Trigonometry Week 6 pp
Fall, Triginometry 5-, Week -7 Chapter. Trigonometry Week pp.-8 What is the TRIGONOMETRY o TrigonometryAngle+ Three sides + triangle + circle. Trigonometry: Measurement of Triangles (derived form Greek
More information1 Graphs of Sine and Cosine
1 Graphs of Sine and Cosine Exercise 1 Sketch a graph of y = cos(t). Label the multiples of π 2 and π 4 on your plot, as well as the amplitude and the period of the function. (Feel free to sketch the unit
More informationMath 3 Trigonometry Part 2 Waves & Laws
Math 3 Trigonometry Part 2 Waves & Laws GRAPHING SINE AND COSINE Graph of sine function: Plotting every angle and its corresponding sine value, which is the y-coordinate, for different angles on the unit
More informationF.A.C.E.S. Language Arts Module
F.A.C.E.S. Language Arts Module Region 17 Education Service Center Dr. Kyle Wargo, Executive Director Department of Special Education Functional Academic Curriculum for Exceptional Students (F.A.C.E.S.)
More informationMaths Revision Booklet. Year 6
Maths Revision Booklet Year 6 Name: Class: 1 Million 1 000 000 six zeros Maths Revision Place Value 750 000 ¾ million 500 000 ½ million 250 000 ¼ million 1.0 = 1 = 0.75 = ¾ = 0.50 = ½ = 0.25 = ¼ = 100
More informationDLS DEF1436. Case 2:13-cv Document Filed in TXSD on 11/19/14 Page 1 of 7 USE CASE SPECIFICATION VIEW ELECTION CERTIFICATE RECORD
Case 2:13-cv-00193 Document 774-32 Filed in TXSD on 11/19/14 Page 1 of 7 An DLS USE CASE SPECIFICATION VIEW ELECTION CERTIFICATE RECORD Texas Department of Public Safety September 13 2013 Version 10 2:13-cv-193
More informationChapter 4/5 Part 2- Trig Identities and Equations
Chapter 4/5 Part 2- Trig Identities and Equations Lesson Package MHF4U Chapter 4/5 Part 2 Outline Unit Goal: By the end of this unit, you will be able to solve trig equations and prove trig identities.
More informationOne of the classes that I have taught over the past few years is a technology course for
Trigonometric Functions through Right Triangle Similarities Todd O. Moyer, Towson University Abstract: This article presents an introduction to the trigonometric functions tangent, cosecant, secant, and
More informationWhile you wait: For a-d: use a calculator to evaluate: Fill in the blank.
While you wait: For a-d: use a calculator to evaluate: a) sin 50 o, cos 40 o b) sin 25 o, cos65 o c) cos o, sin 79 o d) sin 83 o, cos 7 o Fill in the blank. a) sin30 = cos b) cos57 = sin Trigonometric
More informationChapter 4 Trigonometric Functions
Chapter 4 Trigonometric Functions Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Radian and Degree Measure Trigonometric Functions: The Unit Circle Right Triangle Trigonometry
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1316 Ch.1-2 Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Find the supplement of an angle whose
More informationTrigonometric Identities. Copyright 2017, 2013, 2009 Pearson Education, Inc.
5 Trigonometric Identities Copyright 2017, 2013, 2009 Pearson Education, Inc. 1 5.5 Double-Angle Double-Angle Identities An Application Product-to-Sum and Sum-to-Product Identities Copyright 2017, 2013,
More information10.3 Polar Coordinates
.3 Polar Coordinates Plot the points whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > and one with r
More information5-5 Multiple-Angle and Product-to-Sum Identities
Find the values of sin 2, cos 2, and tan 2 for the given value and interval. 1. cos =, (270, 360 ) Since on the interval (270, 360 ), one point on the terminal side of θ has x-coordinate 3 and a distance
More informationGOVERNMENT GAZETTE REPUBLIC OF NAMIBIA
GOVERNMENT GAZETTE OF THE REPUBLIC OF NAMIBIA N$4.40 WINDHOEK - 30 January 2015 No. 5660 CONTENTS Page PROCLAMATION No. 1 Announcement of appointment of P. Unengu as acting judge of High Court of Namibia:
More informationTrigonometric Equations
Chapter Three Trigonometric Equations Solving Simple Trigonometric Equations Algebraically Solving Complicated Trigonometric Equations Algebraically Graphs of Sine and Cosine Functions Solving Trigonometric
More information13-3The The Unit Unit Circle
13-3The The Unit Unit Circle Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Find the measure of the reference angle for each given angle. 1. 120 60 2. 225 45 3. 150 30 4. 315 45 Find the exact value
More information2009 A-level Maths Tutor All Rights Reserved
2 This book is under copyright to A-level Maths Tutor. However, it may be distributed freely provided it is not sold for profit. Contents radians 3 sine, cosine & tangent 7 cosecant, secant & cotangent
More informationF.TF.A.2: Reciprocal Trigonometric Relationships
Regents Exam Questions www.jmap.org Name: If sin x =, a 0, which statement must be true? a ) csc x = a csc x = a ) sec x = a sec x = a 5 The expression sec 2 x + csc 2 x is equivalent to ) sin x ) cos
More informationJim Lambers Math 1B Fall Quarter Final Exam Practice Problems
Jim Lambers Math 1B Fall Quarter 2004-05 Final Exam Practice Problems The following problems are indicative of the types of problems that will appear on the Final Exam, which will be given on Monday, December
More informationTrigonometric Functions
Trigonometric Functions Q1 : Find the radian measures corresponding to the following degree measures: (i) 25 (ii) - 47 30' (iii) 240 (iv) 520 (i) 25 We know that 180 = π radian (ii) â 47 30' â 47 30' =
More information5-5 Multiple-Angle and Product-to-Sum Identities
Find the values of sin 2, cos 2, tan 2 1 cos for the given value interval, (270, 360 ) Since on the interval (270, 360 ), one point on the terminal side of θ has x-coordinate 3 a distance of 5 units from
More informationof the whole circumference.
TRIGONOMETRY WEEK 13 ARC LENGTH AND AREAS OF SECTORS If the complete circumference of a circle can be calculated using C = 2πr then the length of an arc, (a portion of the circumference) can be found by
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation.
More informationName: Period: Date: Math Lab: Explore Transformations of Trig Functions
Name: Period: Date: Math Lab: Explore Transformations of Trig Functions EXPLORE VERTICAL DISPLACEMENT 1] Graph 2] Explain what happens to the parent graph when a constant is added to the sine function.
More informationSection 8.4: The Equations of Sinusoidal Functions
Section 8.4: The Equations of Sinusoidal Functions In this section, we will examine transformations of the sine and cosine function and learn how to read various properties from the equation. Transformed
More informationPrecalculus ~ Review Sheet
Period: Date: Precalculus ~ Review Sheet 4.4-4.5 Multiple Choice 1. The screen below shows the graph of a sound recorded on an oscilloscope. What is the period and the amplitude? (Each unit on the t-axis
More informationcos 2 x + sin 2 x = 1 cos(u v) = cos u cos v + sin u sin v sin(u + v) = sin u cos v + cos u sin v
Concepts: Double Angle Identities, Power Reducing Identities, Half Angle Identities. Memorized: cos x + sin x 1 cos(u v) cos u cos v + sin v sin(u + v) cos v + cos u sin v Derive other identities you need
More informationITEC2620 Introduction to Data Structures
/5/20 ITEC220 Introdution to Dt Strutures Leture 0 Gme Trees Two-Plyer Gmes Rules for gme define the sttespe Nodes re gme sttes Links re possile moves Build serh tree y rute fore Exmple I Exmple II A Our
More informationChapter 6: Periodic Functions
Chapter 6: Periodic Functions In the previous chapter, the trigonometric functions were introduced as ratios of sides of a triangle, and related to points on a circle. We noticed how the x and y values
More informationASSIGNMENT ON TRIGONOMETRY LEVEL 1 (CBSE/NCERT/STATE BOARDS) Find the degree measure corresponding to the following radian measures :
ASSIGNMENT ON TRIGONOMETRY LEVEL 1 (CBSE/NCERT/STATE BOARDS) Find the degree measure corresponding to the following radian measures : (i) c 1 (ii) - c (iii) 6 c (iv) c 11 16 Find the length of an arc of
More informationYou found trigonometric values using the unit circle. (Lesson 4-3)
You found trigonometric values using the unit circle. (Lesson 4-3) LEQ: How do we identify and use basic trigonometric identities to find trigonometric values & use basic trigonometric identities to simplify
More informationAlgebra 2/Trigonometry Review Sessions 1 & 2: Trigonometry Mega-Session. The Unit Circle
Algebra /Trigonometry Review Sessions 1 & : Trigonometry Mega-Session Trigonometry (Definition) - The branch of mathematics that deals with the relationships between the sides and the angles of triangles
More informationMAT01A1. Appendix D: Trigonometry
MAT01A1 Appendix D: Trigonometry Dr Craig 14 February 2017 Introduction Who: Dr Craig What: Lecturer & course coordinator for MAT01A1 Where: C-Ring 508 acraig@uj.ac.za Web: http://andrewcraigmaths.wordpress.com
More informationPROVING IDENTITIES TRIGONOMETRY 4. Dr Adrian Jannetta MIMA CMath FRAS INU0115/515 (MATHS 2) Proving identities 1/ 7 Adrian Jannetta
PROVING IDENTITIES TRIGONOMETRY 4 INU05/55 (MATHS 2) Dr Adrian Jannetta MIMA CMath FRAS Proving identities / 7 Adrian Jannetta Proving an identity Proving an identity is a process which starts with the
More informationSecondary Math Amplitude, Midline, and Period of Waves
Secondary Math 3 7-6 Amplitude, Midline, and Period of Waves Warm UP Complete the unit circle from memory the best you can: 1. Fill in the degrees 2. Fill in the radians 3. Fill in the coordinates in the
More informationChapter 3, Part 1: Intro to the Trigonometric Functions
Haberman MTH 11 Section I: The Trigonometric Functions Chapter 3, Part 1: Intro to the Trigonometric Functions In Example 4 in Section I: Chapter, we observed that a circle rotating about its center (i.e.,
More information