These items need to be included in the notebook. Follow the order listed.
|
|
- Alfred Arnold
- 5 years ago
- Views:
Transcription
1 * Use the provided sheets. * This notebook should be your best written work. Quality counts in this project. Proper notation and terminology is important. We will follow the order used in class. Anyone in a Trigonometry course (or beyond) should to be able to read and understand your material. * You are encouraged to provide examples for your own benefit when using this in the future. There may not be sufficient space to neatly put them on the page itself. Use the back or other paper. These items need to be included in the notebook. Follow the order listed. 1. Definitions of sine and cosine based on the unit circle. Definitions of tangent, cotangent, secant, and cosecant based on sine and cosine.. A completed Unit Circle, Trigonometric Table, and master list of all key trigonometric identities. 3. Complete and accurate graphs of all six trigonometric functions. (Let π = 3 squares.) (List domain, range, and period for all graphs and the amplitude on the applicable graphs.) 4. Complete and accurate graphs of the two types of inverses for each trigonometric function. (example: x = siny and y = arcsinx ) The two types of inverses will be on the same graph together but should be clearly labeled. List the Domain and Range for both types of inverses. (Let π = 3 squares.) 5. Prove the common identities using the order from class. (The list will be provided to you.) 6. Right triangle definitions of the six trigonometric functions (You must include a visual/picture similar triangle connection between the unit circle definitions of sine, cosine, tangent and SohCahToa.) 7. Derive the formulas for area of a non right triangle. (Include the related diagram.) 8. Prove the laws of sines and cosines. (Include the related diagram.) 1
2 1. Definitions of sine and cosine based on the unit circle. Definitions of tangent, cotangent, secant, and cosecant based on sine and cosine.
3 . Unit Circle. For each key point on the unit circle, include the degrees, radians, and coordinates of the associated points. 3
4 . Complete the Trigonometric Table. [ ] 0,π π, π ( π π, ) [ ] 0,π π, π ( 0,π ) Radians Degrees cosθ sinθ tanθ secθ cscθ cotθ π 0 π π 3π π 4
5 . Write in each identity. pythagorean identities (all three) cos(-a) = cos A sin(-a) = - sin A cos(a + B) = cos(a B) = cos( π θ ) = sin( π θ ) = sin(a + B) = sin(a B) = tan (A + B) = tan (A B) = cos A = = = sin A = tan A = Power Reducing Identities: cos θ = sin θ = cos( θ )= sin( θ )= tan( θ )= 5
6 3. Complete and accurate graphs of all six trigonometric functions. (1 sq. = 1 unit. Let π be 3 sq.) (List domain, range, and period for all graphs and the amplitude on the applicable graphs.) y = sinθ y = cscθ D: R: D: R: y = cosθ y = secθ D: R: D: R: y = tanθ y = cotθ D: R: D: R: 6
7 4. Complete and accurate graphs of the two types of inverses for each trigonometric function. (example: x = siny and y = arcsinx ) The two types of inverses will be on the same graph together but should be clearly labeled. List the Domain and Range for both types of inverses. (1 sq. = 1 unit. Let π be 3 sq.) 7
8 5. Prove the common identities. (Follow the order from class. Include a picture if * is shown.) *pythagorean identities (all three) *cos(-a) = cos A *sin(-a) = - sin A 8
9 5. Prove the common identities. (Follow the order from class. Include a picture if * is shown.) * cos( A+ B) = cos Acos B sin Asin B 9
10 5. Prove the common identities. (Follow the order from class.) cos( A B) = cos Acos B+ sin Asin B cos ( ) π θ = sinθ sin ( ) π θ = cosθ sin( A+ B) = sin Acos B+ cos Asin B sin( A B) = sin Acos B cos Asin B 10
11 5. Prove the common identities. (Follow the order from class.) tan A+ tan B tan( A+ B) = 1 tan Atan B tan A tan B tan( A B) = 1 + tan Atan B cos( ) cos sin A = A A = cos A 1 = 1 sin A 11
12 5. Prove the common identities. (Follow the order from class.) sin A= sin Acos A tan A tan A = 1 tan A Power Reducing Identities: = ( + θ) sin θ = 1 ( 1 cos θ) cos θ 1 cos 1 1
13 5. Prove the common identities. (Follow the order from class.) cos( θ )= sin( θ )= tan θ ( ) = ± 1 cosθ = 1+ cosθ sin A 1+ cos A = 1 cos A sin A 13
14 6. Right triangle definitions of the six trigonometric functions (You must include a visual/picture similar triangle connection between the unit circle definitions of sine, cosine, tangent and SohCahToa.) 14
15 7. Derive the formulas for area of a non right triangle. (Include the related diagram.) (Derive two from this diagram and simply list the third case.) 15
16 8. Prove the laws of sines and cosines. (Include the related diagram.) (Proofs follow from the previous page. Prove only one law of cosines but list all three.) 16
Math Section 4.3 Unit Circle Trigonometry
Math 10 - Section 4. Unit Circle Trigonometry An angle is in standard position if its vertex is at the origin and its initial side is along the positive x axis. Positive angles are measured counterclockwise
More informationSection 6.2 Trigonometric Functions: Unit Circle Approach
Section. Trigonometric Functions: Unit Circle Approach The unit circle is a circle of radius centered at the origin. If we have an angle in standard position superimposed on the unit circle, the terminal
More informationUsing the Definitions of the Trigonometric Functions
1.4 Using the Definitions of the Trigonometric Functions Reciprocal Identities Signs and Ranges of Function Values Pythagorean Identities Quotient Identities February 1, 2013 Mrs. Poland Objectives Objective
More informationTrigonometric Ratios. θ + k 360
Trigonometric Ratios These notes are intended as a summary of section 6.1 (p. 466 474) in your workbook. You should also read the section for more complete explanations and additional examples. Coterminal
More informationMA40S Pre-calculus UNIT C Trigonometric Identities CLASS NOTES Analyze Trigonometric Identities Graphically and Verify them Algebraically
1 MA40S Pre-calculus UNIT C Trigonometric Identities CLASS NOTES Analyze Trigonometric Identities Graphically and Verify them Algebraically Definition Trigonometric identity Investigate 1. Using the diagram
More informationChapter 1. Functions 1.3. Trigonometric Functions
1.3 Trigonometric Functions 1 Chapter 1. Functions 1.3. Trigonometric Functions Definition. The number of radians in the central angle A CB within a circle of radius r is defined as the number of radius
More informationCK- 12 Algebra II with Trigonometry Concepts 1
14.1 Graphing Sine and Cosine 1. A.,1 B. (, 1) C. 3,0 D. 11 1, 6 E. (, 1) F. G. H. 11, 4 7, 1 11, 3. 3. 5 9,,,,,,, 4 4 4 4 3 5 3, and, 3 3 CK- 1 Algebra II with Trigonometry Concepts 1 4.ans-1401-01 5.
More informationTrigonometry Trigonometry comes from the Greek word meaning measurement of triangles Angles are typically labeled with Greek letters
Trigonometry Trigonometry comes from the Greek word meaning measurement of triangles Angles are typically labeled with Greek letters α( alpha), β ( beta), θ ( theta) as well as upper case letters A,B,
More informationSolutions for Trigonometric Functions of Any Angle
Solutions for Trigonometric Functions of Any Angle I. Souldatos Answers Problem... Consider the following triangle with AB = and AC =.. Find the hypotenuse.. Find all trigonometric numbers of angle B..
More informationChapter 5: Trigonometric Functions of Angles Homework Solutions
Chapter : Trigonometric Functions of Angles Homework Solutions Section.1 1. D = ( ( 1)) + ( ( )) = + 8 = 100 = 10. D + ( ( )) + ( ( )) = + = 1. (x + ) + (y ) =. (x ) + (y + 7) = r To find the radius, we
More informationHonors Algebra 2 Chapter 14 Page 1
Section. (Introduction) Graphs of Trig Functions Objectives:. To graph basic trig functions using t-bar method. A. Sine and Cosecant. y = sinθ y y y y 0 --- --- 80 --- --- 30 0 0 300 5 35 5 35 60 50 0
More informationMath Analysis Chapter 5 Notes: Analytic Trigonometric
Math Analysis Chapter 5 Notes: Analytic Trigonometric Day 9: Section 5.1-Verifying Trigonometric Identities Fundamental Trig Identities Reciprocal Identities: 1 1 1 sin u = cos u = tan u = cscu secu cot
More informationMore with Angles Reference Angles
More with Angles Reference Angles A reference angle is the angle formed by the terminal side of an angle θ, and the (closest) x axis. A reference angle, θ', is always 0 o
More informationMath 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
Names Date. Consider the function Math 0550 Worksheet SHOW ALL OF YOUR WORK! f() = + 6 + 7 (a) Complete the square and write the function in the form f() = ( a) + b. f() = + 6 + 7 = + 6 + ( 6 ) ( 6 ) +
More informationPreview from Notesale.co.uk Page 2 of 42
. CONCEPTS & FORMULAS. INTRODUCTION Radian The angle subtended at centre of a circle by an arc of length equal to the radius of the circle is radian r o = o radian r r o radian = o = 6 Positive & Negative
More information(c) cos Arctan ( 3) ( ) PRECALCULUS ADVANCED REVIEW FOR FINAL FIRST SEMESTER
PRECALCULUS ADVANCED REVIEW FOR FINAL FIRST SEMESTER Work the following on notebook paper ecept for the graphs. Do not use our calculator unless the problem tells ou to use it. Give three decimal places
More information2 Trigonometric functions
Theodore Voronov. Mathematics 1G1. Autumn 014 Trigonometric functions Trigonometry provides methods to relate angles and lengths but the functions we define have many other applications in mathematics..1
More informationSect 7.4 Trigonometric Functions of Any Angles
Sect 7.4 Trigonometric Functions of Any Angles Objective #: Extending the definition to find the trigonometric function of any angle. Before we can extend the definition our trigonometric functions, we
More informationLesson 33 - Trigonometric Identities. Pre-Calculus
Lesson 33 - Trigonometric Identities Pre-Calculus 1 (A) Review of Equations An equation is an algebraic statement that is true for only several values of the variable The linear equation 5 = 2x 3 is only
More informationA-Level Mathematics TRIGONOMETRY. G. David Boswell - R2S Explore 2019
A-Level Mathematics TRIGONOMETRY G. David Boswell - R2S Explore 2019 1. Graphs the functions sin kx, cos kx, tan kx, where k R; In these forms, the value of k determines the periodicity of the trig functions.
More informationFUNDAMENTAL TRIGONOMETRIC INDENTITIES 1 = cos. sec θ 1 = sec. = cosθ. Odd Functions sin( t) = sint. csc( t) = csct tan( t) = tant
NOTES 8: ANALYTIC TRIGONOMETRY Name: Date: Period: Mrs. Nguyen s Initial: LESSON 8.1 TRIGONOMETRIC IDENTITIES FUNDAMENTAL TRIGONOMETRIC INDENTITIES Reciprocal Identities sinθ 1 cscθ cosθ 1 secθ tanθ 1
More informationCrash Course in Trigonometry
Crash Course in Trigonometry Dr. Don Spickler September 5, 003 Contents 1 Trigonometric Functions 1 1.1 Introduction.................................... 1 1. Right Triangle Trigonometry...........................
More informationMath Worksheet 1. f(x) = (x a) 2 + b. = x 2 6x = (x 2 6x + 9) = (x 3) 2 1
Names Date Math 00 Worksheet. Consider the function f(x) = x 6x + 8 (a) Complete the square and write the function in the form f(x) = (x a) + b. f(x) = x 6x + 8 ( ) ( ) 6 6 = x 6x + + 8 = (x 6x + 9) 9
More informationPrentice Hall: Algebra 2 with Trigonometry 2006 Correlated to: California Mathematics Content Standards for Trigonometry (Grades 9-12)
California Mathematics Content Standards for Trigonometry (Grades 9-12) Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric
More informationACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER / Trigonometry
ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH0000 SEMESTER 1 017/018 DR. ANTHONY BROWN 5. Trigonometry 5.1. Parity and Co-Function Identities. In Section 4.6 of Chapter 4 we looked
More informationTHE COMPOUND ANGLE IDENTITIES
TRIGONOMETRY THE COMPOUND ANGLE IDENTITIES Question 1 Prove the validity of each of the following trigonometric identities. a) sin x + cos x 4 4 b) cos x + + 3 sin x + 2cos x 3 3 c) cos 2x + + cos 2x cos
More informationSET 1. (1) Solve for x: (a) e 2x = 5 3x
() Solve for x: (a) e x = 5 3x SET We take natural log on both sides: ln(e x ) = ln(5 3x ) x = 3 x ln(5) Now we take log base on both sides: log ( x ) = log (3 x ln 5) x = log (3 x ) + log (ln(5)) x x
More informationPre- Calculus Mathematics Trigonometric Identities and Equations
Pre- Calculus Mathematics 12 6.1 Trigonometric Identities and Equations Goal: 1. Identify the Fundamental Trigonometric Identities 2. Simplify a Trigonometric Expression 3. Determine the restrictions on
More informationAnalytic Trigonometry. Copyright Cengage Learning. All rights reserved.
Analytic Trigonometry Copyright Cengage Learning. All rights reserved. 7.4 Basic Trigonometric Equations Copyright Cengage Learning. All rights reserved. Objectives Basic Trigonometric Equations Solving
More informationSection 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?
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? In relationship to a circle, if I go half way around the edge
More informationI.e., the range of f(x) = arctan(x) is all real numbers y such that π 2 < y < π 2
Inverse Trigonometric Functions: The inverse sine function, denoted by fx = arcsinx or fx = sin 1 x is defined by: y = sin 1 x if and only if siny = x and π y π I.e., the range of fx = arcsinx is all real
More informationWarm Up = = 9 5 3) = = ) ) 99 = ) Simplify. = = 4 6 = 2 6 3
Warm Up Simplify. 1) 99 = 3 11 2) 125 + 2 20 = 5 5 + 4 5 = 9 5 3) 2 + 7 2 + 3 7 = 4 + 6 7 + 2 7 + 21 4) 4 42 3 28 = 4 3 3 2 = 4 6 6 = 25 + 8 7 = 2 6 3 Test Results Average Median 5 th : 76.5 78 7 th :
More informationMATH 100 REVIEW PACKAGE
SCHOOL OF UNIVERSITY ARTS AND SCIENCES MATH 00 REVIEW PACKAGE Gearing up for calculus and preparing for the Assessment Test that everybody writes on at. You are strongly encouraged not to use a calculator
More informationMATH 2412 Sections Fundamental Identities. Reciprocal. Quotient. Pythagorean
MATH 41 Sections 5.1-5.4 Fundamental Identities Reciprocal Quotient Pythagorean 5 Example: If tanθ = and θ is in quadrant II, find the exact values of the other 1 trigonometric functions using only fundamental
More informationMath Section 4.3 Unit Circle Trigonometry
Math 10 - Section 4. Unit Circle Trigonometry An angle is in standard position if its vertex is at the origin and its initial side is along the positive x axis. Positive angles are measured counterclockwise
More informationLesson 22 - Trigonometric Identities
POP QUIZ Lesson - Trigonometric Identities IB Math HL () Solve 5 = x 3 () Solve 0 = x x 6 (3) Solve = /x (4) Solve 4 = x (5) Solve sin(θ) = (6) Solve x x x x (6) Solve x + = (x + ) (7) Solve 4(x ) = (x
More information3.1 Fundamental Identities
www.ck.org Chapter. Trigonometric Identities and Equations. Fundamental Identities Introduction We now enter into the proof portion of trigonometry. Starting with the basic definitions of sine, cosine,
More informationPrecalculus Review. Functions to KNOW! 1. Polynomial Functions. Types: General form Generic Graph and unique properties. Constants. Linear.
Precalculus Review Functions to KNOW! 1. Polynomial Functions Types: General form Generic Graph and unique properties Constants Linear Quadratic Cubic Generalizations for Polynomial Functions - The domain
More informationJUST THE MATHS SLIDES NUMBER 3.1. TRIGONOMETRY 1 (Angles & trigonometric functions) A.J.Hobson
JUST THE MATHS SLIDES NUMBER 3.1 TRIGONOMETRY 1 (Angles & trigonometric functions) by A.J.Hobson 3.1.1 Introduction 3.1.2 Angular measure 3.1.3 Trigonometric functions UNIT 3.1 - TRIGONOMETRY 1 - ANGLES
More information2. Pythagorean Theorem:
Chapter 4 Applications of Trigonometric Functions 4.1 Right triangle trigonometry; Applications 1. A triangle in which one angle is a right angle (90 0 ) is called a. The side opposite the right angle
More informationSection 5.4 The Other Trigonometric Functions
Section 5.4 The Other Trigonometric Functions Section 5.4 The Other Trigonometric Functions In the previous section, we defined the e and coe functions as ratios of the sides of a right triangle in a circle.
More informationTrigonometry.notebook. March 16, Trigonometry. hypotenuse opposite. Recall: adjacent
Trigonometry Recall: hypotenuse opposite adjacent 1 There are 3 other ratios: the reciprocals of sine, cosine and tangent. Secant: Cosecant: (cosec θ) Cotangent: 2 Example: Determine the value of x. a)
More informationA. Incorrect! For a point to lie on the unit circle, the sum of the squares of its coordinates must be equal to 1.
Algebra - Problem Drill 19: Basic Trigonometry - Right Triangle No. 1 of 10 1. Which of the following points lies on the unit circle? (A) 1, 1 (B) 1, (C) (D) (E), 3, 3, For a point to lie on the unit circle,
More information1) SSS 2) SAS 3) ASA 4) AAS Never: SSA and AAA Triangles with no right angles.
NOTES 6 & 7: TRIGONOMETRIC FUNCTIONS OF ANGLES AND OF REAL NUMBERS Name: Date: Mrs. Nguyen s Initial: LESSON 6.4 THE LAW OF SINES Review: Shortcuts to prove triangles congruent Definition of Oblique Triangles
More informationMATH 1316 REVIEW FOR FINAL EXAM
MATH 116 REVIEW FOR FINAL EXAM Problem Answer 1. Find the complete solution (to the nearest tenth) if 4.5, 4.9 sinθ-.9854497 and 0 θ < π.. Solve sin θ 0, if 0 θ < π. π π,. How many solutions does cos θ
More informationChapter 4 Trigonometric Functions
Chapter 4 Trigonometric Functions Overview: 4.1 Radian and Degree Measure 4.2 Trigonometric Functions: The Unit Circle 4.3 Right Triangle Trigonometry 4.4 Trigonometric Functions of Any Angle 4.5 Graphs
More informationPractice Questions for Midterm 2 - Math 1060Q - Fall 2013
Eam Review Practice Questions for Midterm - Math 060Q - Fall 0 The following is a selection of problems to help prepare ou for the second midterm eam. Please note the following: anthing from Module/Chapter
More informationand sinθ = cosb =, and we know a and b are acute angles, find cos( a+ b) Trigonometry Topics Accuplacer Review revised July 2016 sin.
Trigonometry Topics Accuplacer Revie revised July 0 You ill not be alloed to use a calculator on the Accuplacer Trigonometry test For more information, see the JCCC Testing Services ebsite at http://jcccedu/testing/
More informationMTH 112: Elementary Functions
1/19 MTH 11: Elementary Functions Section 6.6 6.6:Inverse Trigonometric functions /19 Inverse Trig functions 1 1 functions satisfy the horizontal line test: Any horizontal line crosses the graph of a 1
More informationAnalytic Trigonometry. Copyright Cengage Learning. All rights reserved.
Analytic Trigonometry Copyright Cengage Learning. All rights reserved. 7.1 Trigonometric Identities Copyright Cengage Learning. All rights reserved. Objectives Simplifying Trigonometric Expressions Proving
More informationTrigonometry: Graphs of trig functions (Grade 10) *
OpenStax-CNX module: m39414 1 Trigonometry: Graphs of trig functions (Grade 10) * Free High School Science Texts Project This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution
More informationMonroe Township High School Mathematics Department
To: AP Calculus AB Re: Summer Project 017 Date: June 017 Monroe Township High School Mathematics Department To help begin your study of Calculus, you will be required to complete a review project this
More informationNotes on Radian Measure
MAT 170 Pre-Calculus Notes on Radian Measure Radian Angles Terri L. Miller Spring 009 revised April 17, 009 1. Radian Measure Recall that a unit circle is the circle centered at the origin with a radius
More informationInverse Trig Functions
6.6i Inverse Trigonometric Functions Inverse Sine Function Does g(x) = sin(x) have an inverse? What restriction would we need to make so that at least a piece of this function has an inverse? Given f (x)
More informationAs we know, the three basic trigonometric functions are as follows: Figure 1
Trigonometry Basic Functions As we know, the three basic trigonometric functions are as follows: sin θ = cos θ = opposite hypotenuse adjacent hypotenuse tan θ = opposite adjacent Where θ represents an
More informationChapter 3. Radian Measure and Circular Functions. Copyright 2005 Pearson Education, Inc.
Chapter 3 Radian Measure and Circular Functions Copyright 2005 Pearson Education, Inc. 3.1 Radian Measure Copyright 2005 Pearson Education, Inc. Measuring Angles Thus far we have measured angles in degrees
More informationTopic Outline for Algebra 2 & and Trigonometry One Year Program
Topic Outline for Algebra 2 & and Trigonometry One Year Program Algebra 2 & and Trigonometry - N - Semester 1 1. Rational Expressions 17 Days A. Factoring A2.A.7 B. Rationals A2.N.3 A2.A.17 A2.A.16 A2.A.23
More informationCore Mathematics 3 Trigonometry
Edexcel past paper questions Core Mathematics 3 Trigonometry Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Maths 3 Trigonometry Page 1 C3 Trigonometry In C you were introduced to radian measure
More information1. Trigonometry.notebook. September 29, Trigonometry. hypotenuse opposite. Recall: adjacent
Trigonometry Recall: hypotenuse opposite adjacent 1 There are 3 other ratios: the reciprocals of sine, cosine and tangent. Secant: Cosecant: (cosec θ) Cotangent: 2 Example: Determine the value of x. a)
More informationNYS Algebra II and Trigonometry Suggested Sequence of Units (P.I's within each unit are NOT in any suggested order)
1 of 6 UNIT P.I. 1 - INTEGERS 1 A2.A.1 Solve absolute value equations and inequalities involving linear expressions in one variable 1 A2.A.4 * Solve quadratic inequalities in one and two variables, algebraically
More informationPrecalculus Midterm Review
Precalculus Midterm Review Date: Time: Length of exam: 2 hours Type of questions: Multiple choice (4 choices) Number of questions: 50 Format of exam: 30 questions no calculator allowed, then 20 questions
More informationA List of Definitions and Theorems
Metropolitan Community College Definition 1. Two angles are called complements if the sum of their measures is 90. Two angles are called supplements if the sum of their measures is 180. Definition 2. One
More informationPreCalculus First Semester Exam Review
PreCalculus First Semester Eam Review Name You may turn in this eam review for % bonus on your eam if all work is shown (correctly) and answers are correct. Please show work NEATLY and bo in or circle
More informationAMB121F Trigonometry Notes
AMB11F Trigonometry Notes Trigonometry is a study of measurements of sides of triangles linked to the angles, and the application of this theory. Let ABC be right-angled so that angles A and B are acute
More informationChapter 5 Analytic Trigonometry
Chapter 5 Analytic Trigonometry Overview: 5.1 Using Fundamental Identities 5.2 Verifying Trigonometric Identities 5.3 Solving Trig Equations 5.4 Sum and Difference Formulas 5.5 Multiple-Angle and Product-to-sum
More informationChapter 5 Trigonometric Functions of Angles
Chapter 5 Trigonometric Functions of Angles Section 3 Points on Circles Using Sine and Cosine Signs Signs I Signs (+, +) I Signs II (+, +) I Signs II (, +) (+, +) I Signs II (, +) (+, +) I III Signs II
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. and θ is in quadrant IV. 1)
Chapter 5-6 Review Math 116 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the fundamental identities to find the value of the trigonometric
More informationAnalytic Trigonometry
Chapter 5 Analytic Trigonometry Course Number Section 5.1 Using Fundamental Identities Objective: In this lesson you learned how to use fundamental trigonometric identities to evaluate trigonometric functions
More informationMATH 32 FALL 2012 FINAL EXAM - PRACTICE EXAM SOLUTIONS
MATH 2 FALL 2012 FINAL EXAM - PRACTICE EXAM SOLUTIONS (1) ( points) Solve the equation x 1 =. Solution: Since x 1 =, x 1 = or x 1 =. Solving for x, x = 4 or x = 2. (2) In the triangle below, let a = 4,
More informationUsing this definition, it is possible to define an angle of any (positive or negative) measurement by recognizing how its terminal side is obtained.
Angle in Standard Position With the Cartesian plane, we define an angle in Standard Position if it has its vertex on the origin and one of its sides ( called the initial side ) is always on the positive
More informationTrigonometric Functions. Copyright Cengage Learning. All rights reserved.
4 Trigonometric Functions Copyright Cengage Learning. All rights reserved. 4.3 Right Triangle Trigonometry Copyright Cengage Learning. All rights reserved. What You Should Learn Evaluate trigonometric
More informationPublic Assessment of the HKDSE Mathematics Examination
Public Assessment of the HKDSE Mathematics Examination. Exam Format (a) The examination consists of one paper. (b) All questions are conventional questions. (c) The duration is hours and 30 minutes. Section
More informationPractice Questions for Midterm 2 - Math 1060Q Fall
Eam Review Practice Questions for Midterm - Math 00Q - 0Fall The following is a selection of problems to help prepare ou for the second midterm eam. Please note the following: there ma be mistakes the
More informationMATH 130 FINAL REVIEW
MATH 130 FINAL REVIEW Problems 1 5 refer to triangle ABC, with C=90º. Solve for the missing information. 1. A = 40, c = 36m. B = 53 30', b = 75mm 3. a = 91 ft, b = 85 ft 4. B = 1, c = 4. ft 5. A = 66 54',
More informationPART I: NO CALCULATOR (144 points)
Math 10 Practice Final Trigonometry 11 th edition Lial, Hornsby, Schneider, and Daniels (Ch. 1-8) PART I: NO CALCULATOR (1 points) (.1,.,.,.) For the following functions: a) Find the amplitude, the period,
More information7.3 Inverse Trigonometric Functions
58 transcendental functions 73 Inverse Trigonometric Functions We now turn our attention to the inverse trigonometric functions, their properties and their graphs, focusing on properties and techniques
More informationREQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS
REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS The Department of Applied Mathematics administers a Math Placement test to assess fundamental skills in mathematics that are necessary to begin the study
More informationUnit 3 Trigonometry Note Package. Name:
MAT40S Unit 3 Trigonometry Mr. Morris Lesson Unit 3 Trigonometry Note Package Homework 1: Converting and Arc Extra Practice Sheet 1 Length 2: Unit Circle and Angles Extra Practice Sheet 2 3: Determining
More informationTrig. Trig is also covered in Appendix C of the text. 1SOHCAHTOA. These relations were first introduced
Trig Trig is also covered in Appendix C of the text. 1SOHCAHTOA These relations were first introduced for a right angled triangle to relate the angle,its opposite and adjacent sides and the hypotenuse.
More informationsecθ 1 cosθ The pythagorean identities can also be expressed as radicals
Basic Identities Section Objectives: Students will know how to use fundamental trigonometric identities to evaluate trigonometric functions and simplify trigonometric expressions. We use trig. identities
More informationSection 6.2 Notes Page Trigonometric Functions; Unit Circle Approach
Section Notes Page Trigonometric Functions; Unit Circle Approach A unit circle is a circle centered at the origin with a radius of Its equation is x y = as shown in the drawing below Here the letter t
More informationUnit Circle. Return to. Contents
Unit Circle Return to Table of Contents 32 The Unit Circle The circle x 2 + y 2 = 1, with center (0,0) and radius 1, is called the unit circle. Quadrant II: x is negative and y is positive (0,1) 1 Quadrant
More information4-3 Trigonometric Functions on the Unit Circle
Find the exact value of each trigonometric function, if defined. If not defined, write undefined. 9. sin The terminal side of in standard position lies on the positive y-axis. Choose a point P(0, 1) on
More informationπ π π π Trigonometry Homework Booklet 1. Convert 5.3 radians to degrees. A B C D Determine the period of 15
Trigonometry Homework Booklet 1. Convert 5.3 radians to degrees. A. 0.09 B. 0.18 C. 151.83 D. 303.67. Determine the period of y = 6cos x + 8. 15 15 A. B. C. 15 D. 30 15 3. Determine the exact value of
More informationweebly.com/ Core Mathematics 3 Trigonometry
http://kumarmaths. weebly.com/ Core Mathematics 3 Trigonometry Core Maths 3 Trigonometry Page 1 C3 Trigonometry In C you were introduced to radian measure and had to find areas of sectors and segments.
More informationOne of the powerful themes in trigonometry is that the entire subject emanates from a very simple idea: locating a point on the unit circle.
2.24 Tanz and the Reciprocals Derivatives of Other Trigonometric Functions One of the powerful themes in trigonometry is that the entire subject emanates from a very simple idea: locating a point on the
More information(Section 4.7: Inverse Trig Functions) 4.82 PART F: EVALUATING INVERSE TRIG FUNCTIONS. Think:
PART F: EVALUATING INVERSE TRIG FUNCTIONS Think: (Section 4.7: Inverse Trig Functions) 4.82 A trig function such as sin takes in angles (i.e., real numbers in its domain) as inputs and spits out outputs
More information1 Chapter 2 Perform arithmetic operations with polynomial expressions containing rational coefficients 2-2, 2-3, 2-4
NYS Performance Indicators Chapter Learning Objectives Text Sections Days A.N. Perform arithmetic operations with polynomial expressions containing rational coefficients. -, -5 A.A. Solve absolute value
More informationChapter 5 The Next Wave: MORE MODELING AND TRIGONOMETRY
ANSWERS Mathematics (Mathematical Analysis) page 1 Chapter The Next Wave: MORE MODELING AND TRIGONOMETRY NW-1. TI-8, points; Casio, points a) An infinite number of them. b) 17p, - 7p c) Add p n to p, p
More informationSince 1 revolution = 1 = = Since 1 revolution = 1 = =
Fry Texas A&M University Math 150 Chapter 8A Fall 2015! 207 Since 1 revolution = 1 = = Since 1 revolution = 1 = = Convert to revolutions (or back to degrees and/or radians) a) 45! = b) 120! = c) 450! =
More informationTopic Outline for Integrated Algebra 2 and Trigonometry-R One Year Program with Regents in June
Topic Outline for Integrated Algebra 2 and Trigonometry-R One Year Program with Regents in June Integrated Algebra 2 & Trigonometry - R Semester 1 1. Rational Expressions 7 Days A. Factoring A2.A.7 Factor
More informationMPE Review Section II: Trigonometry
MPE Review Section II: Trigonometry Review similar triangles, right triangles, and the definition of the sine, cosine and tangent functions of angles of a right triangle In particular, recall that the
More informationVectors and Geometry
Vectors and Geometry Vectors In the context of geometry, a vector is a triplet of real numbers. In applications to a generalized parameters space, such as the space of random variables in a reliability
More information( ) ( ) ( ) ( ) MATHEMATICS Precalculus Martin Huard Fall 2007 Semester Review. 1. Simplify each expression. 4a b c. x y. 18x. x 2x.
MATHEMATICS 0-009-0 Precalculus Martin Huard Fall 007. Simplif each epression. a) 8 8 g) ( ) ( j) m) a b c a b 8 8 8 n f) t t ) h) + + + + k) + + + n) + + + + + ( ) i) + n 8 + 9 z + l) 8 o) ( + ) ( + )
More information*n23494b0220* C3 past-paper questions on trigonometry. 1. (a) Given that sin 2 θ + cos 2 θ 1, show that 1 + tan 2 θ sec 2 θ. (2)
C3 past-paper questions on trigonometry physicsandmathstutor.com June 005 1. (a) Given that sin θ + cos θ 1, show that 1 + tan θ sec θ. (b) Solve, for 0 θ < 360, the equation tan θ + secθ = 1, giving your
More informationC3 Exam Workshop 2. Workbook. 1. (a) Express 7 cos x 24 sin x in the form R cos (x + α) where R > 0 and 0 < α < 2
C3 Exam Workshop 2 Workbook 1. (a) Express 7 cos x 24 sin x in the form R cos (x + α) where R > 0 and 0 < α < 2 π. Give the value of α to 3 decimal places. (b) Hence write down the minimum value of 7 cos
More informationUNIT 2 ALGEBRA II TEMPLATE CREATED BY REGION 1 ESA UNIT 2
UNIT 2 ALGEBRA II TEMPLATE CREATED BY REGION 1 ESA UNIT 2 Algebra II Unit 2 Overview: Trigonometric Functions Building on their previous work with functions, and on their work with trigonometric ratios
More informationPractice Problems for MTH 112 Exam 2 Prof. Townsend Fall 2013
Practice Problems for MTH 11 Exam Prof. Townsend Fall 013 The problem list is similar to problems found on the indicated pages. means I checked my work on my TI-Nspire software Pages 04-05 Combine the
More informationI IV II III 4.1 RADIAN AND DEGREE MEASURES (DAY ONE) COMPLEMENTARY angles add to90 SUPPLEMENTARY angles add to 180
4.1 RADIAN AND DEGREE MEASURES (DAY ONE) TRIGONOMETRY: the study of the relationship between the angles and sides of a triangle from the Greek word for triangle ( trigonon) (trigonon ) and measure ( metria)
More informationTrigonometry LESSON SIX - Trigonometric Identities I Lesson Notes
LESSON SIX - Trigonometric Identities I Example Understanding Trigonometric Identities. a) Why are trigonometric identities considered to be a special type of trigonometric equation? Trigonometric Identities
More information