Course I. Lesson 5 Trigonometric Functions (II) 5A Radian Another Unit of Angle Graphs of Trigonometric Functions
|
|
- Noah Jenkins
- 5 years ago
- Views:
Transcription
1 Course I Lesson 5 Trigonometric Functions (II) 5A Radian Another Unit of Angle Graphs of Trigonometric Functions
2 Radian Degree ( ) Angle of /0 of one circle 0 is a familiar number in astronom. ( ne ear = 5da 0 ) Radian (non-dimention) Angle is described b the ratio of the arc to the radius. r Arc 0 = r Radius A pure number (no unit) but smbol rad is used. rad=57.9 ( Memorize 0 = rad. ) B rad r r A
3 Merits of Radian Eample : Epression becomes simple. Area of a sector with angle and radius r [degree] : r 0 [rad] : = r r r Eample : Values of trigonometric functions of a small angle can be obtained approimatel. When angle is small BH arcab sin = = B B EX. sin = H A (From Table, deg 0.075) B
4 Graphs of the Sine/Cosine Functions r sin = cos = r r = r sin = r cos r = = sin = cos P P 4
5 Graph of the Tangent Function r tan = = = tan P 5
6 Periodic Function Periodic function A function f () is said to be periodic with period p if we have f ( + p) = f ( ) Namel, the values of a function repeat themselves regularl. Eamples Find the period of the sine functions = sin Period = +
7 r Eample Eample. Illustrate the following functions and show their periods () () () Ans. = sin () Epansion in the -direction (period =) = sin = sin = sin = sin - () Epansion in the -direction (period =) = sin = sin () Shift in the -direction (period =) = sin = sin 7
8 Eercise Eercise. Answer about the following function = sin( ) ( 0 ) () When dos this function becomes zero? () What are the values of this function at =0, () Illustrate this function. Ans. Pause the video and solve the problem. 8
9 Eercise Eercise. Answer about the following function = sin( ) ( 0 ) () When does this function become zero? () What are the values of this function at =0, () Illustrate this function. Ans. () 0, 0 4, 4 Therefore becomes zero at = 0,,, =,, () At = 0 : = sin( ) = At = : = sin(4 ) = sin( ) = () , 5 Ahh! That s so eas! 9
10 Course I Lesson 5 Trigonometric Functions (II) 5B Trigonometric Equation Trigonometric Inequalit 0
11 Trigonometric Equation A trigonometric equation is an equation that contains unknown trigonometric function. E. sin + cos = 0 This kind of equation is true for certain angles. [Note] A trigonometric equation that holds true for an angle is called a trigonometric identit, which we will stud net lesson. Some trigonometric equation can be solved easil b using algebra ideas, while others ma not be solved eactl but approimatel. Eample sin = This can be easil solved. See net slide. Eample Roots and can be found numericall (See the figure). 0 sin = 0 = sin =
12 Eample Eample. Solve the following trigonometric equation. sin = 0 Ans. Step We first look at sin solve as we did before. Step Recall the graph of the value of - 5 = sin sin = which satisf this epression. = = sin as being the variable of the equation a from 0 to or a unit circle, and obt Ⅱ Ⅲ, 5 5 Ⅰ Ⅳ Step Considering the periodicit, add n. 5 = + n, + n
13 Trigonometric Inequalit A trigonometric inequalit is an inequalit that contains unknown trigonometric function. It can be solved based on a trigonometric e Eample. Solve the following trigonometric equation. sin > 0 Ans. Step Convert the given inequalit to a trigonometric equation b replacing sign to equalit sign. sin = 0 Step Solve the resulting equation in the interval [0, ] = /, 5 / = sin = 5 Step Among intervals divided b the obtained roots, find the intervals wh 5 satisf the trigonometric inequalit. < < Step 4 Etend 5 the soltion to the whole domain. + n < < + n
14 Eercise Eercise. Solve the following trigonometric equation. sin + cos = 0 Ans. Pause the video and solve the problem. 4
15 Eercise Eercise. Solve the following trigonometric equation. sin + cos = 0 0 Ans. sin Put + cos = 0 X = cos sin + cos = From ( X ) + X X =, X = cos = = 0, = 0 X X + = 0 ( X )(X ) = 0 From cos = =,
16 Eercise Eercise. Solve the following trigonometric inequalit tan Ans. Pause the video and solve the problem.
17 Answer to the Eercise Eercise. Solve the following trigonometric inequalit tan Ans. The corresponding trigonometric equation is tan = Tangent has the period as shown in the figure. In the interval [-/, /], the root is = 4 From the graph and considering the periodicit, the solution is + n < + n 4-7 7
Unit 4 Trigonometry. Study Notes 1 Right Triangle Trigonometry (Section 8.1)
Unit 4 Trigonometr Stud Notes 1 Right Triangle Trigonometr (Section 8.1) Objective: Evaluate trigonometric functions of acute angles. Use a calculator to evaluate trigonometric functions. Use trigonometric
More informationPolar Functions Polar coordinates
548 Chapter 1 Parametric, Vector, and Polar Functions 1. What ou ll learn about Polar Coordinates Polar Curves Slopes of Polar Curves Areas Enclosed b Polar Curves A Small Polar Galler... and wh Polar
More information4.1 Angles and Angle Measure. 1, multiply by
4.1 Angles and Angle Measure Angles can be measured in degrees or radians. Angle measures without units are considered to be in radians. Radian: One radian is the measure of the central angle subtended
More information13 Trigonometric Graphs
Trigonometric Graphs Concepts: Period The Graph of the sin, cos, tan, csc, sec, and cot Functions Appling Graph Transformations to the Graphs of the sin, cos, tan, csc, sec, and cot Functions Using Graphical
More information14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio.
14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio. Using the space below, draw at least right triangles, each of which has one
More informationUnit 6 Introduction to Trigonometry The Unit Circle (Unit 6.3)
Unit Introduction to Trigonometr The Unit Circle Unit.) William Bill) Finch Mathematics Department Denton High School Introduction Trig Functions Circle Quadrental Angles Other Angles Unit Circle Periodic
More information4.7 INVERSE TRIGONOMETRIC FUNCTIONS
Section 4.7 Inverse Trigonometric Functions 4 4.7 INVERSE TRIGONOMETRIC FUNCTIONS NASA What ou should learn Evaluate and graph the inverse sine function. Evaluate and graph the other inverse trigonometric
More informationContents. How You May Use This Resource Guide
Contents How You Ma Use This Resource Guide ii 0 Trigonometric Formulas, Identities, and Equations Worksheet 0.: Graphical Analsis of Trig Identities.............. Worksheet 0.: Verifing Trigonometric
More informationA Quick Review of Trigonometry
A Quick Review of Trigonometry As a starting point, we consider a ray with vertex located at the origin whose head is pointing in the direction of the positive real numbers. By rotating the given ray (initial
More informationSum and Difference Identities. Cosine Sum and Difference Identities: cos A B. does NOT equal cos A. Cosine of a Sum or Difference. cos B.
7.3 Sum and Difference Identities 7-1 Cosine Sum and Difference Identities: cos A B Cosine of a Sum or Difference cos cos does NOT equal cos A cos B. AB AB EXAMPLE 1 Finding Eact Cosine Function Values
More information3.7 Graphing Linear Inequalities
8 CHAPTER Graphs and Functions.7 Graphing Linear Inequalities S Graph Linear Inequalities. Graph the Intersection or Union of Two Linear Inequalities. Graphing Linear Inequalities Recall that the graph
More informationEngineering and Construction F3HV 11 Maths Craft 1 RIGHT ANGLED TRIANGLES : PYTHAGORAS' THEOREM
RIGHT NGLED TRINGLES : PYTHGORS' THEOREM ver important triangle, in terms of practical use, is the right-angled triangle. In the "real" world, the right-angled triangle is used etensivel. It is a shape
More informationIntroduction to Trigonometric Functions. Peggy Adamson and Jackie Nicholas
Mathematics Learning Centre Introduction to Trigonometric Functions Pegg Adamson and Jackie Nicholas c 998 Universit of Sdne Acknowledgements A significant part of this manuscript has previousl appeared
More informationApplying trigonometric functions
Appling trigonometric functions Sllabus Guide hapter 8 ontents 8. Degrees and radians 8. Trigonometric ratios and the unit circle 8. Trigonometric graphs 8. Trigonometric functions and applications hapter
More information4.1: Angles & Angle Measure
4.1: Angles & Angle Measure In Trigonometry, we use degrees to measure angles in triangles. However, degree is not user friendly in many situations (just as % is not user friendly unless we change it into
More informationUnit 7: Trigonometry Part 1
100 Unit 7: Trigonometry Part 1 Right Triangle Trigonometry Hypotenuse a) Sine sin( α ) = d) Cosecant csc( α ) = α Adjacent Opposite b) Cosine cos( α ) = e) Secant sec( α ) = c) Tangent f) Cotangent tan(
More informationName Class Date. subtract 3 from each side. w 5z z 5 2 w p - 9 = = 15 + k = 10m. 10. n =
Reteaching Solving Equations To solve an equation that contains a variable, find all of the values of the variable that make the equation true. Use the equalit properties of real numbers and inverse operations
More informationChapter 3: Section 3-2 Graphing Linear Inequalities
Chapter : Section - Graphing Linear Inequalities D. S. Malik Creighton Universit, Omaha, NE D. S. Malik Creighton Universit, Omaha, NE Chapter () : Section - Graphing Linear Inequalities / 9 Geometric
More informationMath12 Pre-Calc Review - Trig
Math1 Pre-Calc Review - Trig Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following angles, in degrees, is coterminal with, but not equal
More information: Find the values of the six trigonometric functions for θ. Special Right Triangles:
ALGEBRA 2 CHAPTER 13 NOTES Section 13-1 Right Triangle Trig Understand and use trigonometric relationships of acute angles in triangles. 12.F.TF.3 CC.9- Determine side lengths of right triangles by using
More informationModule 2, Section 2 Graphs of Trigonometric Functions
Principles of Mathematics Section, Introduction 5 Module, Section Graphs of Trigonometric Functions Introduction You have studied trigonometric ratios since Grade 9 Mathematics. In this module ou will
More informationDate Lesson Text TOPIC Homework. Getting Started Pg. 314 # 1-7. Radian Measure and Special Angles Sine and Cosine CAST
UNIT 5 TRIGONOMETRIC FUNCTIONS Date Lesson Text TOPIC Homework Oct. 0 5.0 (50).0 Getting Started Pg. # - 7 Nov. 5. (5). Radian Measure Angular Velocit Pg. 0 # ( 9)doso,,, a Nov. 5 Nov. 5. (5) 5. (5)..
More informationTrigonometric Graphs. Graphs of Sine and Cosine
Trigonometric Graphs Page 1 4 Trigonometric Graphs Graphs of Sine and Cosine In Figure 13, we showed the graphs of = sin and = cos, for angles from 0 rad to rad. In reality these graphs extend indefinitely
More informationTrigonometric Functions of Any Angle
Trigonometric Functions of Any Angle MATH 160, Precalculus J. Robert Buchanan Department of Mathematics Fall 2011 Objectives In this lesson we will learn to: evaluate trigonometric functions of any angle,
More informationName: Teacher: Pd: Algebra 2/Trig: Trigonometric Graphs (SHORT VERSION)
Algebra 2/Trig: Trigonometric Graphs (SHORT VERSION) In this unit, we will Learn the properties of sine and cosine curves: amplitude, frequency, period, and midline. Determine what the parameters a, b,
More informationUnit 2 Intro to Angles and Trigonometry
HARTFIELD PRECALCULUS UNIT 2 NOTES PAGE 1 Unit 2 Intro to Angles and Trigonometry This is a BASIC CALCULATORS ONLY unit. (2) Definition of an Angle (3) Angle Measurements & Notation (4) Conversions of
More informationSecondary Math 3- Honors. 7-4 Inverse Trigonometric Functions
Secondary Math 3- Honors 7-4 Inverse Trigonometric Functions Warm Up Fill in the Unit What You Will Learn How to restrict the domain of trigonometric functions so that the inverse can be constructed. How
More information5.6 Translations and Combinations of Transformations
5.6 Translations and Combinations of Transformations The highest tides in the world are found in the Ba of Fund. Tides in one area of the ba cause the water level to rise to 6 m above average sea level
More information13.2. General Angles and Radian Measure. What you should learn
Page 1 of 1. General Angles and Radian Measure What ou should learn GOAL 1 Measure angles in standard position using degree measure and radian measure. GOAL Calculate arc lengths and areas of sectors,
More informationStudent Instruction Sheet: Unit 4, Lesson 3. Primary Trigonometric Ratios
Student Instruction Sheet: Unit 4, Lesson 3 Suggested Time: 75 minutes Primary Trigonometric Ratios What s important in this lesson: In this lesson, you will use trigonometry (sin, cos, tan) to measure
More information1. The Pythagorean Theorem
. The Pythagorean Theorem The Pythagorean theorem states that in any right triangle, the sum of the squares of the side lengths is the square of the hypotenuse length. c 2 = a 2 b 2 This theorem can be
More informationMath-2 Lesson 8-7: Unit 5 Review (Part -2)
Math- Lesson 8-7: Unit 5 Review (Part -) Trigonometric Functions sin cos A A SOH-CAH-TOA Some old horse caught another horse taking oats away. opposite ( length ) o sin A hypotenuse ( length ) h SOH adjacent
More informationSyllabus Objective: 3.1 The student will solve problems using the unit circle.
Precalculus Notes: Unit 4 Trigonometr Sllabus Objective:. The student will solve problems using the unit circle. Review: a) Convert. hours into hours and minutes. Solution: hour + (0.)(60) = hour and minutes
More informationTrigonometric Identities
Trigonometric Identities 6.5 SKILL BUILDER An equation that is true for all alues of the ariable in it is called an identit. For instance, the epression 4( 3) 8 is an eample of an algebraic identit because
More informationMath 12 Final Review Quiz 3
Math 12 Final Review Quiz 3 Multiple Choice Identify the choice that best completes the statement answers the question. 1. What is the measure of the reference angle f an angle of in standard position?
More information4.6 Graphs of Other Trigonometric Functions
.6 Graphs of Other Trigonometric Functions Section.6 Graphs of Other Trigonometric Functions 09 Graph of the Tangent Function Recall that the tangent function is odd. That is, tan tan. Consequentl, the
More informationTriangle Trigonometry
Honors Finite/Brief: Trigonometry review notes packet Triangle Trigonometry Right Triangles All triangles (including non-right triangles) Law of Sines: a b c sin A sin B sin C Law of Cosines: a b c bccos
More informationEssential Question What are the characteristics of the graph of the tangent function?
8.5 Graphing Other Trigonometric Functions Essential Question What are the characteristics of the graph of the tangent function? Graphing the Tangent Function Work with a partner. a. Complete the table
More informationLesson 5 1 Objectives
Time For Trigonometry!!! Degrees, Radians, Revolutions Arc Length, Area of Sectors SOHCAHTOA Unit Circle Graphs of Sine, Cosine, Tangent Law of Cosines Law of Sines Lesson 5 1 Objectives Convert between
More informationCollege Technical Math 2
WTCS Repository 10-804-116 College Technical Math 2 Course Outcome Summary Course Information Description Topics include: vectors; trigonometric functions and their graphs; identities; exponential and
More informationEXPANDING THE CALCULUS HORIZON. Robotics
EXPANDING THE CALCULUS HORIZON Robotics Robin designs and sells room dividers to defra college epenses. She is soon overwhelmed with orders and decides to build a robot to spra paint her dividers. As in
More informationMath 144 Activity #2 Right Triangle Trig and the Unit Circle
1 p 1 Right Triangle Trigonometry Math 1 Activity #2 Right Triangle Trig and the Unit Circle We use right triangles to study trigonometry. In right triangles, we have found many relationships between the
More information2.2 Limit of a Function and Limit Laws
Limit of a Function and Limit Laws Section Notes Page Let s look at the graph y What is y()? That s right, its undefined, but what if we wanted to find the y value the graph is approaching as we get close
More informationIB SL Review Questions
I SL Review Questions. Solve the equation 3 cos x = 5 sin x, for x in the interval 0 x 360, giving your answers to the nearest degree.. Given that sin θ =, cos θ = 3 and 0 < θ < 360, find the value of
More informationTrigonometry I. Exam 0
Trigonometry I Trigonometry Copyright I Standards 006, Test Barry Practice Mabillard. Exam 0 www.math0s.com 1. The minimum and the maximum of a trigonometric function are shown in the diagram. a) Write
More informationGraphing square root functions. What would be the base graph for the square root function? What is the table of values?
Unit 3 (Chapter 2) Radical Functions (Square Root Functions Sketch graphs of radical functions b appling translations, stretches and reflections to the graph of Analze transformations to identif the of
More informationSection 14: Trigonometry Part 1
Section 14: Trigonometry Part 1 The following Mathematics Florida Standards will be covered in this section: MAFS.912.F-TF.1.1 MAFS.912.F-TF.1.2 MAFS.912.F-TF.1.3 Understand radian measure of an angle
More informationChapter Three Chapter Three
Chapter Three Chapter Three 90 CHAPTER THREE ConcepTests for Section.. If f () = g (), then f() = g(). (a) True (b) False (b). If f () = g (), then f() = g() + C, where C is some constant. You might point
More informationApplications of Differentiation
Contents 1 Applications of Differentiation 1.1 Tangents and Normals 1. Maima and Minima 14 1. The Newton-Raphson Method 8 1.4 Curvature 47 1.5 Differentiation of Vectors 54 1.6 Case Stud: Comple Impedance
More information{ x + 2 if x < Study Guide and Intervention. Special Functions
NAME DATE PERID -6 Stud Guide and Intervention Piecewise-Defined Functions A piecewise-defined function is written using two or more epressions. Its graph is often disjointed. Eample Graph f() = if < {
More informationUnit 3, Lesson 1.3 Special Angles in the Unit Circle
Unit, Lesson Special Angles in the Unit Circle Special angles exist within the unit circle For these special angles, it is possible to calculate the exact coordinates for the point where the terminal side
More informationMATHEMATICS FOR ENGINEERING TRIGONOMETRY
MATHEMATICS FOR ENGINEERING TRIGONOMETRY TUTORIAL SOME MORE RULES OF TRIGONOMETRY This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves
More informationTable of Contents. Unit 5: Trigonometric Functions. Answer Key...AK-1. Introduction... v
These materials ma not be reproduced for an purpose. The reproduction of an part for an entire school or school sstem is strictl prohibited. No part of this publication ma be transmitted, stored, or recorded
More informationAppendix D Trigonometry
Math 151 c Lynch 1 of 8 Appendix D Trigonometry Definition. Angles can be measure in either degree or radians with one complete revolution 360 or 2 rad. Then Example 1. rad = 180 (a) Convert 3 4 into degrees.
More informationTrigonometry and the Unit Circle. Chapter 4
Trigonometry and the Unit Circle Chapter 4 Topics Demonstrate an understanding of angles in standard position, expressed in degrees and radians. Develop and apply the equation of the unit circle. Solve
More informationReview sheet inches centimeters 40. Name: Class: Date:
Name: Class: Date:.-.2 Review sheet Multiple Choice Identify the choice that best completes the statement or answers the question.. Find the complement of the following angle. Round your answer to two
More informationIntermediate Algebra. Gregg Waterman Oregon Institute of Technology
Intermediate Algebra Gregg Waterman Oregon Institute of Technolog c 2017 Gregg Waterman This work is licensed under the Creative Commons Attribution 4.0 International license. The essence of the license
More informationPre-calculus Chapter 4 Part 1 NAME: P.
Pre-calculus NAME: P. Date Day Lesson Assigned Due 2/12 Tuesday 4.3 Pg. 284: Vocab: 1-3. Ex: 1, 2, 7-13, 27-32, 43, 44, 47 a-c, 57, 58, 63-66 (degrees only), 69, 72, 74, 75, 78, 79, 81, 82, 86, 90, 94,
More informationCHECK Your Understanding
CHECK Your Understanding. State the domain and range of each relation. Then determine whether the relation is a function, and justif our answer.. a) e) 5(, ), (, 9), (, 7), (, 5), (, ) 5 5 f) 55. State
More informationMath General Angles, Radian Measure, measures of arcs and sectors
Math-3 6-3 General Angles, Radian Measure, measures of arcs and sectors tan 5 9 5 h cos? 9 ϴ Tangent ratio gives sides of a right triangle. h h h 5 9 5 81 106 cos cos 9 106 9 106 106 cos 3 10 opp 10 sin?
More informationIntegrating ICT into mathematics at KS4&5
Integrating ICT into mathematics at KS4&5 Tom Button tom.button@mei.org.uk www.mei.org.uk/ict/ This session will detail the was in which ICT can currentl be used in the teaching and learning of Mathematics
More informationUnit 2: Trigonometry. This lesson is not covered in your workbook. It is a review of trigonometry topics from previous courses.
Unit 2: Trigonometry This lesson is not covered in your workbook. It is a review of trigonometry topics from previous courses. Pythagorean Theorem Recall that, for any right angled triangle, the square
More informationReview of Trigonometry
Worksheet 8 Properties of Trigonometric Functions Section Review of Trigonometry This section reviews some of the material covered in Worksheets 8, and The reader should be familiar with the trig ratios,
More informationUnit 13: Periodic Functions and Trig
Date Period Unit 13: Periodic Functions and Trig Day Topic 0 Special Right Triangles and Periodic Function 1 Special Right Triangles Standard Position Coterminal Angles 2 Unit Circle Cosine & Sine (x,
More informationTrigonometry is concerned with the connection between the sides and angles in any right angled triangle.
Trigonometry Obj: I can to use trigonometry to find unknown sides and unknown angles in a triangle. Trigonometry is concerned with the connection between the sides and angles in any right angled triangle.
More informationA trigonometric ratio is a,
ALGEBRA II Chapter 13 Notes The word trigonometry is derived from the ancient Greek language and means measurement of triangles. Section 13.1 Right-Triangle Trigonometry Objectives: 1. Find the trigonometric
More informationA Formal Definition of Limit
5 CHAPTER Limits and Their Properties L + ε L L ε (c, L) c + δ c c δ The - definition of the it of f as approaches c Figure. A Formal Definition of Limit Let s take another look at the informal description
More informationCHAPTER 3, FORM E TRIGONOMETRY Choose the best answer. NAME DATE. Do not use a calculator for problems 1-11.
CHAPTER, FORM E TRIGONOMETRY Choose the best answer. NAME DATE Do not use a calculator for problems 1-11. 1. Which of the following describes the measures of 1. all angles that are coterminal with the
More informationTrigonometry Review Day 1
Name Trigonometry Review Day 1 Algebra II Rotations and Angle Terminology II Terminal y I Positive angles rotate in a counterclockwise direction. Reference Ray Negative angles rotate in a clockwise direction.
More informationDerivatives 3: The Derivative as a Function
Derivatives : The Derivative as a Function 77 Derivatives : The Derivative as a Function Model : Graph of a Function 9 8 7 6 5 g() - - - 5 6 7 8 9 0 5 6 7 8 9 0 5 - - -5-6 -7 Construct Your Understanding
More informationWeek 27 Algebra 1 Assignment:
Week 7 Algebra Assignment: Da : p. 494 #- odd, -, 8- Da : pp. 496-497 #-9 odd, -6 Da : pp. 0-0 #-9 odd, -, -9 Da 4: p. 09 #-4, 7- Da : pp. - #-9 odd Notes on Assignment: Page 494: General notes for this
More informationVerify Trigonometric Identities
4.3 a., A..A; P..C TEKS Verify Trigonometric Identities Before You graphed trigonometric functions. Now You will verify trigonometric identities. Why? So you can model the path of Halley s comet, as in
More informationChoose the correct answer below. 2. Convert the angle to a decimal in degrees.
1. Choose the figure that shows an angle of in standard position. Choose the correct answer below. 2. Convert the angle to a decimal in degrees. (Do not round until the final answer. Then round to two
More information2.8 Distance and Midpoint Formulas; Circles
Section.8 Distance and Midpoint Formulas; Circles 9 Eercises 89 90 are based on the following cartoon. B.C. b permission of Johnn Hart and Creators Sndicate, Inc. 89. Assuming that there is no such thing
More informationProving Trigonometric Identities
MHF 4UI Unit 7 Day Proving Trigonometric Identities An identity is an epression which is true for all values in the domain. Reciprocal Identities csc θ sin θ sec θ cos θ cot θ tan θ Quotient Identities
More informationSECTION 6-8 Graphing More General Tangent, Cotangent, Secant, and Cosecant Functions
6-8 Graphing More General Tangent, Cotangent, Secant, and Cosecant Functions 9 duce a scatter plot in the viewing window. Choose 8 for the viewing window. (B) It appears that a sine curve of the form k
More informationMATHEMATICS 105 Plane Trigonometry
Chapter I THE TRIGONOMETRIC FUNCTIONS MATHEMATICS 105 Plane Trigonometry INTRODUCTION The word trigonometry literally means triangle measurement. It is concerned with the measurement of the parts, sides,
More information3 Coordinates. 3.1 Prologue
3 Coordinates 3. Prologue Coordinates describe the location of a point or an object using numbers. If ou are shipwrecked somewhere off the coast of Patagonia and radioing for help, ou can sa, I am somewhere
More informationPart Five: Trigonometry Review. Trigonometry Review
T.5 Trigonometry Review Many of the basic applications of physics, both to mechanical systems and to the properties of the human body, require a thorough knowledge of the basic properties of right triangles,
More informationThe Quadratic function f(x) = x 2 2x 3. y y = x 2 2x 3. We will now begin to study the graphs of the trig functions, y = sinx, y = cosx and y = tanx.
Chapter 7 Trigonometric Graphs Introduction We have alread looked at the graphs of various functions : The Linear function f() = The Quadratic function f() = The Hperbolic function f() = = = = We will
More informationGraphing Trigonometric Functions
LESSON Graphing Trigonometric Functions Graphing Sine and Cosine UNDERSTAND The table at the right shows - and f ()-values for the function f () 5 sin, where is an angle measure in radians. Look at the
More informationMath 1330 Test 3 Review Sections , 5.1a, ; Know all formulas, properties, graphs, etc!
Math 1330 Test 3 Review Sections 4.1 4.3, 5.1a, 5. 5.4; Know all formulas, properties, graphs, etc! 1. Similar to a Free Response! Triangle ABC has right angle C, with AB = 9 and AC = 4. a. Draw and label
More informationCopyrighted by Gabriel Tang B.Ed., B.Sc. Page 167.
lgebra Chapter 8: nalytical Trigonometry 8- Inverse Trigonometric Functions Chapter 8: nalytical Trigonometry Inverse Trigonometric Function: - use when we are given a particular trigonometric ratio and
More informationSolve 3-D problems using Pythagoras theorem and trigonometric ratios (A*) Solve more complex 2-D problems using Pythagoras theorem & trigonometry (A)
Moving from A to A* Solve 3-D problems using Pythagoras theorem and trigonometric ratios (A*) A* Use the sine & cosine rules to solve more complex problems involving non right-angled triangles (A*) Find
More informationis a plane curve and the equations are parametric equations for the curve, with parameter t.
MATH 2412 Sections 6.3, 6.4, and 6.5 Parametric Equations and Polar Coordinates. Plane Curves and Parametric Equations Suppose t is contained in some interval I of the real numbers, and = f( t), = gt (
More informationApplications of Trigonometric and Circular Functions
CHAPTER OBJECTIVES Applications of Trigonometric and Circular Functions Stresses in the earth compress rock formations and cause them to buckle into sinusoidal shapes. It is important for geologists to
More informationMath 144 Activity #3 Coterminal Angles and Reference Angles
144 p 1 Math 144 Activity #3 Coterminal Angles and Reference Angles For this activity we will be referring to the unit circle. Using the unit circle below, explain how you can find the sine of any given
More informationSection 2.2: Absolute Value Functions, from College Algebra: Corrected Edition by Carl Stitz, Ph.D. and Jeff Zeager, Ph.D. is available under a
Section.: Absolute Value Functions, from College Algebra: Corrected Edition b Carl Stitz, Ph.D. and Jeff Zeager, Ph.D. is available under a Creative Commons Attribution-NonCommercial-ShareAlike.0 license.
More informationDownloaded from
Top Concepts Class XI: Maths Ch : Trigonometric Function Chapter Notes. An angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final
More informationObjectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right triangle using
Ch 13 - RIGHT TRIANGLE TRIGONOMETRY Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right triangle using trigonometric
More informationTransformations. which the book introduces in this chapter. If you shift the graph of y 1 x to the left 2 units and up 3 units, the
CHAPTER 8 Transformations Content Summar In Chapter 8, students continue their work with functions, especiall nonlinear functions, through further stud of function graphs. In particular, the consider three
More information8B.2: Graphs of Cosecant and Secant
Opp. Name: Date: Period: 8B.: Graphs of Cosecant and Secant Or final two trigonometric functions to graph are cosecant and secant. Remember that So, we predict that there is a close relationship between
More informationSection 6.2 Graphs of the Other Trig Functions
Section 62 Graphs of the Other Trig Functions 369 Section 62 Graphs of the Other Trig Functions In this section, we will explore the graphs of the other four trigonometric functions We ll begin with the
More informationName Student Activity
Open the TI-Nspire document Proofs_of_Identities.tns. An identity is an equation that is true for all values of the variables for which both sides of the equation are defined. In this activity, you will
More information3.9 Differentials. Tangent Line Approximations. Exploration. Using a Tangent Line Approximation
3.9 Differentials 3 3.9 Differentials Understand the concept of a tangent line approimation. Compare the value of the differential, d, with the actual change in,. Estimate a propagated error using a differential.
More information1. y = f(x) y = f(x + 3) 3. y = f(x) y = f(x 1) 5. y = 3f(x) 6. y = f(3x) 7. y = f(x) 8. y = f( x) 9. y = f(x 3) + 1
.7 Transformations.7. Eercises To see all of the help resources associated with this section, click OSttS Chapter b. Suppose (, ) is on the graph of = f(). In Eercises - 8, use Theorem.7 to find a point
More informationROCKWOOD CURRICULUM WRITING PROCESS OVERVIEW
ROCKWOOD CURRICULUM WRITING PROCESS OVERVIEW Course Content Area Last Update for this Course Trigonometry Mathematics February 2009 Results of Program Evaluation Program Evaluation Recommendations Continue
More information6.8 Sine ing and Cosine ing It
SECONDARY MATH III // MODULE 6 In the previous tasks of this module you have used the similarity of circles, the symmetry of circles, right triangle trigonometry and proportional reasoning to locate stakes
More informationAPPENDIX A: Trigonometry Basics
APPENDIX A: Trigonometr Basics Trigonometr Basics A Degree Measure A Right-Triangle Trigonometr A4 Unit-Circle Trigonometr A Radian Measure A0 Angle Measure Conversions A4 Sine and Cosine Functions A5
More informationName Parent Function Library Date Sheilah Chason Math 444
Name Parent Function Librar Date Sheilah Chason Math Objective: To neatl create a librar of Parent Functions that ou will refer to during this unit. Some of the functions ou are ver familiar with, some
More information