5.4 Graphs of the Sine & Cosine Functions Objectives
|
|
|
- Winifred Nash
- 5 years ago
- Views:
Transcription
1 Objectives 1. Graph Functions of the Form y = A sin(wx) Using Transformations. 2. Graph Functions of the Form y = A cos(wx) Using Transformations. 3. Determine the Amplitude & Period of Sinusoidal Functions. 4. Graph Sinusoidal Functions Using Key Points. 5. Find an Equation for a Sinusoidal Graph. 30 August Kidoguchi, Kenneth
2 The Graph of the Sine Function y = sin(x) Over One Cycle 30 August Kidoguchi, Kenneth
3 The Graph of the Sine Function y = sin(q) Over One Cycle 30 August Kidoguchi, Kenneth
4 30 August Kidoguchi, Kenneth
5 1. Graph Functions of the Form y = A sin(wx) w/ Transformations Example: Graph y = 5 sin(x) using transformations. Use the graph to determine the domain and the range of y = 5 sin(x). 30 August Kidoguchi, Kenneth
6 1. Graph Functions of the Form y = A sin(wx) w/ Transformations Example: Graph y = ½ sin(-p x) using transformations. Use the graph to determine the domain and the range of y = ½ sin(-p x). 30 August Kidoguchi, Kenneth
7 The Graph of the Cosine Function y = cos(x) Over One Cycle 30 August Kidoguchi, Kenneth
8 The Graph of the Cosine Function y = cos(q) Over One Cycle 30 August Kidoguchi, Kenneth
9 30 August Kidoguchi, Kenneth
10 2. Graph Functions of the Form y = A cos(wx) w/ Transformations Example: Graph y = -cos(2x) using transformations. Use the graph to determine the domain and the range of y = -cos(2x). 30 August Kidoguchi, Kenneth
11 Sinusoidal Graphs sin x cos x p 2 30 August Kidoguchi, Kenneth
12 Amplitude and Period of a Sinusoidal Function If w > 0, the amplitude and period of: y = A sin(wx) and y = A cos(wx) are: Amplitude A and Period = T = 2p/w Example: Determine the amplitude and period of y = 4 cos (3x). 30 August Kidoguchi, Kenneth
13 Steps for Graphing a Sinusoidal Function of the Form y = A sin(wx) or y = A cos(wx) Using Key Points STEP 1: Determine the amplitude and period of the sinusoidal function. STEP 2: Divide the interval [0, 2p/w] into four subintervals of the same length. STEP 3: Use the endpoints of these subintervals to obtain five key points on the graph. STEP 4: Plot the five key points with a sinusoidal graph of one cycle. Extend the graph in each direction to make it complete. Example: Graph y = 4 sin (2x) using key points over one cycle. 30 August Kidoguchi, Kenneth
14 STEP 1: STEP 2: STEP 3: STEP 4: Example: Graph y = 4 sin (2x) using key points over one cycle. 30 August Kidoguchi, Kenneth
15 Steps for Graphing a Sinusoidal Function of the Form y = A sin(wx) or y = A cos(wx) Using Key Points STEP 1: Determine the amplitude and period of the sinusoidal function. STEP 2: Divide the interval [0, 2p/w] into four subintervals of the same length. STEP 3: Use the endpoints of these subintervals to obtain five key points on the graph. STEP 4: Plot the five key points with a sinusoidal graph of one cycle. Extend the graph in each direction to make it complete. p y 5cos x 2 Example: Graph using key points over one cycle. 30 August Kidoguchi, Kenneth
16 Steps for Graphing a Sinusoidal Function of the Form y = A sin(wx) or y = A cos(wx) Using Key Points STEP 1: Determine the amplitude and period of the sinusoidal function. STEP 2: Divide the interval [0, 2p/w] into four subintervals of the same length. STEP 3: Use the endpoints of these subintervals to obtain five key points on the graph. STEP 4: Plot the five key points with a sinusoidal graph of one cycle. Extend the graph in each direction to make it complete. p y 3cos x 1 2 Example: Graph using key points over one cycle. 30 August Kidoguchi, Kenneth
17 5. Find an Equation for a Sinusoidal Graph - Example Find a sinusoidal function g(x) whose graph would appear as shown. 30 August Kidoguchi, Kenneth
Section 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
Section 8.4 Equations of Sinusoidal Functions soln.notebook. May 17, Section 8.4: The Equations of Sinusoidal Functions.
Section 8.4: The Equations of Sinusoidal Functions Stop Sine 1 In this section, we will examine transformations of the sine and cosine function and learn how to read various properties from the equation.
Graphing Sine and Cosine
The problem with average monthly temperatures on the preview worksheet is an example of a periodic function. Periodic functions are defined on p.254 Periodic functions repeat themselves each period. The
The Sine Function. Precalculus: Graphs of Sine and Cosine
Concepts: Graphs of Sine, Cosine, Sinusoids, Terminology (amplitude, period, phase shift, frequency). The Sine Function Domain: x R Range: y [ 1, 1] Continuity: continuous for all x Increasing-decreasing
5.1 Graphing Sine and Cosine Functions.notebook. Chapter 5: Trigonometric Functions and Graphs
Chapter 5: Trigonometric Functions and Graphs 1 Chapter 5 5.1 Graphing Sine and Cosine Functions Pages 222 237 Complete the following table using your calculator. Round answers to the nearest tenth. 2
Section 5.2 Graphs of the Sine and Cosine Functions
Section 5.2 Graphs of the Sine and Cosine Functions We know from previously studying the periodicity of the trigonometric functions that the sine and cosine functions repeat themselves after 2 radians.
Section 7.6 Graphs of the Sine and Cosine Functions
4 Section 7. Graphs of the Sine and Cosine Functions In this section, we will look at the graphs of the sine and cosine function. The input values will be the angle in radians so we will be using x is
Algebra and Trig. I. The graph of
Algebra and Trig. I 4.5 Graphs of Sine and Cosine Functions The graph of The graph of. The trigonometric functions can be graphed in a rectangular coordinate system by plotting points whose coordinates
the input values of a function. These are the angle values for trig functions
SESSION 8: TRIGONOMETRIC FUNCTIONS KEY CONCEPTS: Graphs of Trigonometric Functions y = sin θ y = cos θ y = tan θ Properties of Graphs Shape Intercepts Domain and Range Minimum and maximum values Period
Chapter #2 test sinusoidal function
Chapter #2 test sinusoidal function Sunday, October 07, 2012 11:23 AM Multiple Choice [ /10] Identify the choice that best completes the statement or answers the question. 1. For the function y = sin x,
Graphs of sin x and cos x
Graphs of sin x and cos x One cycle of the graph of sin x, for values of x between 0 and 60, is given below. 1 0 90 180 270 60 1 It is this same shape that one gets between 60 and below). 720 and between
3. Use your unit circle and fill in the exact values of the cosine function for each of the following angles (measured in radians).
Graphing Sine and Cosine Functions Desmos Activity 1. Use your unit circle and fill in the exact values of the sine function for each of the following angles (measured in radians). sin 0 sin π 2 sin π
1 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
Practice Test 3 (longer than the actual test will be) 1. Solve the following inequalities. Give solutions in interval notation. (Expect 1 or 2.
MAT 115 Spring 2015 Practice Test 3 (longer than the actual test will be) Part I: No Calculators. Show work. 1. Solve the following inequalities. Give solutions in interval notation. (Expect 1 or 2.) a.
Secondary 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
Graph of the Sine Function
1 of 6 8/6/2004 6.3 GRAPHS OF THE SINE AND COSINE 6.3 GRAPHS OF THE SINE AND COSINE Periodic Functions Graph of the Sine Function Graph of the Cosine Function Graphing Techniques, Amplitude, and Period
5.3 Trigonometric Graphs. Copyright Cengage Learning. All rights reserved.
5.3 Trigonometric Graphs Copyright Cengage Learning. All rights reserved. Objectives Graphs of Sine and Cosine Graphs of Transformations of Sine and Cosine Using Graphing Devices to Graph Trigonometric
MATH 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
2.4 Translating Sine and Cosine Functions
www.ck1.org Chapter. Graphing Trigonometric Functions.4 Translating Sine and Cosine Functions Learning Objectives Translate sine and cosine functions vertically and horizontally. Identify the vertical
Graphing Trig Functions. Objectives: Students will be able to graph sine, cosine and tangent functions and translations of these functions.
Graphing Trig Functions Name: Objectives: Students will be able to graph sine, cosine and tangent functions and translations of these functions. y = sinx (0,) x 0 sinx (,0) (0, ) (,0) /2 3/2 /2 3/2 2 x
Section 2.4 General Sinusoidal Graphs
Section. General Graphs Objective: any one of the following sets of information about a sinusoid, find the other two: ) the equation ) the graph 3) the amplitude, period or frequency, phase displacement,
4-4 Graphing Sine and Cosine Functions
Describe how the graphs of f (x) and g(x) are related. Then find the amplitude of g(x), and sketch two periods of both functions on the same coordinate axes. 1. f (x) = sin x; g(x) = sin x The graph of
You analyzed graphs of functions. (Lesson 1-5)
You analyzed graphs of functions. (Lesson 1-5) LEQ: How do we graph transformations of the sine and cosine functions & use sinusoidal functions to solve problems? sinusoid amplitude frequency phase shift
Name: Which equation is represented in the graph? Which equation is represented by the graph? 1. y = 2 sin 2x 2. y = sin x. 1.
Name: Print Close Which equation is represented in the graph? Which equation is represented by the graph? y = 2 sin 2x y = sin x y = 2 sin x 4. y = sin 2x Which equation is represented in the graph? 4.
Section 7.1 Graphs of Sine and Cosine
Section 7.1 Graphs of Sine and Cosine OBJECTIVE 1: Understanding the Graph of the Sine Function and its Properties In Chapter 7, we will use a rectangular coordinate system for a different purpose. We
6.4 & 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
WARM UP. 1. Expand the expression (x 2 + 3) Factor the expression x 2 2x Find the roots of 4x 2 x + 1 by graphing.
WARM UP Monday, December 8, 2014 1. Expand the expression (x 2 + 3) 2 2. Factor the expression x 2 2x 8 3. Find the roots of 4x 2 x + 1 by graphing. 1 2 3 4 5 6 7 8 9 10 Objectives Distinguish between
SECTION 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
Extra Practice for Section I: Chapter 4
Haberman MTH 112 Extra Practice for Section I: Chapter You should complete all of these problems without a calculator in order to prepare for the Midterm which is a no-calculator exam. 1. Find two different
http://www.math.utah.edu/~palais/sine.html http://www.ies.co.jp/math/java/trig/index.html http://www.analyzemath.com/function/periodic.html http://math.usask.ca/maclean/sincosslider/sincosslider.html http://www.analyzemath.com/unitcircle/unitcircle.html
Functions Modeling Change A Preparation for Calculus Third Edition
Powerpoint slides copied from or based upon: Functions Modeling Change A Preparation for Calculus Third Edition Connally, Hughes-Hallett, Gleason, Et Al. Copyright 2007 John Wiley & Sons, Inc. 1 CHAPTER
Amplitude, Reflection, and Period
SECTION 4.2 Amplitude, Reflection, and Period Copyright Cengage Learning. All rights reserved. Learning Objectives 1 2 3 4 Find the amplitude of a sine or cosine function. Find the period of a sine or
Math 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
Unit 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.
2.5 Amplitude, Period and Frequency
2.5 Amplitude, Period and Frequency Learning Objectives Calculate the amplitude and period of a sine or cosine curve. Calculate the frequency of a sine or cosine wave. Graph transformations of sine and
5.3-The Graphs of the Sine and Cosine Functions
5.3-The Graphs of the Sine and Cosine Functions Objectives: 1. Graph the sine and cosine functions. 2. Determine the amplitude, period and phase shift of the sine and cosine functions. 3. Find equations
Section 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
Section 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions In this section, we will look at the graphs of the other four trigonometric functions. We will start by examining the tangent
Precalculus 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
Please grab the warm up off of the chair in the front of the room and begin working!
Please grab the warm up off of the chair in the front of the room and begin working! add the x! #2 Fix to y = 5cos (2πx 2) + 9 Have your homework out on your desk to be checked. (Pre requisite for graphing
Copyright 2009 Pearson Education, Inc. Slide Section 8.2 and 8.3-1
8.3-1 Transformation of sine and cosine functions Sections 8.2 and 8.3 Revisit: Page 142; chapter 4 Section 8.2 and 8.3 Graphs of Transformed Sine and Cosine Functions Graph transformations of y = sin
cos 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
The Formula for Sinusoidal Signals
The Formula for I The general formula for a sinusoidal signal is x(t) =A cos(2pft + f). I A, f, and f are parameters that characterize the sinusoidal sinal. I A - Amplitude: determines the height of the
5-5 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
Section 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:
5-5 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
Section 5.2 Graphs of the Sine and Cosine Functions
A Periodic Function and Its Period Section 5.2 Graphs of the Sine and Cosine Functions A nonconstant function f is said to be periodic if there is a number p > 0 such that f(x + p) = f(x) for all x in
Unit 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,
Name: 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.
Unit 5 Graphing Trigonmetric Functions
HARTFIELD PRECALCULUS UNIT 5 NOTES PAGE 1 Unit 5 Graphing Trigonmetric Functions This is a BASIC CALCULATORS ONLY unit. (2) Periodic Functions (3) Graph of the Sine Function (4) Graph of the Cosine Function
1. 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
Chapter 7 Repetitive Change: Cyclic Functions
Chapter 7 Repetitive Change: Cyclic Functions 7.1 Cycles and Sine Functions Data that is periodic may often be modeled by trigonometric functions. This chapter will help you use Excel to deal with periodic
Unit 3 Unit Circle and Trigonometry + Graphs
HARTFIELD PRECALCULUS UNIT 3 NOTES PAGE 1 Unit 3 Unit Circle and Trigonometry + Graphs (2) The Unit Circle (3) Displacement and Terminal Points (5) Significant t-values Coterminal Values of t (7) Reference
Sect 4.5 Inequalities Involving Quadratic Function
71 Sect 4. Inequalities Involving Quadratic Function Objective #0: Solving Inequalities using a graph Use the graph to the right to find the following: Ex. 1 a) Find the intervals where f(x) > 0. b) Find
Exam: Friday 4 th May How to Revise. What to use to revise:
National 5 Mathematics Exam Revision Questions Exam: Friday 4 th May 2018 How to Revise Use this booklet for homework Come to after school revision classes Come to the Easter holiday revision class There
Trig Graphs. What is a Trig graph? This is the graph of a trigonometrical function e.g.
Trig Graphs What is a Trig graph? This is the graph of a trigonometrical function e.g. sin, cos or tan How do we draw one? We make a table of value using the calculator. Tr to complete the one below (work
Math 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
Math 1330 Precalculus Electronic Homework (EHW 6) Sections 5.1 and 5.2.
Math 0 Precalculus Electronic Homework (EHW 6) Sections 5. and 5.. Work the following problems and choose the correct answer. The problems that refer to the Textbook may be found at www.casa.uh.edu in
Pythagorean 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
PreCalc: 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
Chapter 6: Periodic Functions
Chapter 6: Periodic Functions In the previous chapter, the trigonometric functions were introduced as ratios of sides of a right triangle, and related to points on a circle. We noticed how the x and y
Name: Date: Group: Learning Target: I can determine amplitude, period, frequency, and phase shift, given a graph or equation of a periodic function.
Pre-Lesson Assessment Unit 2: Trigonometric Functions Periodic Functions Diagnostic Exam: Page 1 Name: Date: Group: Learning Target: I can determine amplitude, period, frequency, and phase shift, given
Figure 1. The unit circle.
TRIGONOMETRY PRIMER This document will introduce (or reintroduce) the concept of trigonometric functions. These functions (and their derivatives) are related to properties of the circle and have many interesting
In this section, you will learn how to use a graph or a list of properties of the desired function to write a corresponding equation.
5.4 Graphing and Modelling With = a sin [k(x d)] + c and = a cos [k(x d)] + c In order to model a real-world situation using a sine or a cosine function, ou must analse the situation and then transform
2009 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
MATH 105: Midterm #1 Practice Problems
Name: MATH 105: Midterm #1 Practice Problems 1. TRUE or FALSE, plus explanation. Give a full-word answer TRUE or FALSE. If the statement is true, explain why, using concepts and results from class to justify
( x "1) 2 = 25, x 3 " 2x 2 + 5x "12 " 0, 2sin" =1.
Unit Analytical Trigonometry Classwork A) Verifying Trig Identities: Definitions to know: Equality: a statement that is always true. example:, + 7, 6 6, ( + ) 6 +0. Equation: a statement that is conditionally
Year 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
of 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
CHAPTER 14 ALTERNATING VOLTAGES AND CURRENTS
CHAPTER 4 ALTERNATING VOLTAGES AND CURRENTS Exercise 77, Page 28. Determine the periodic time for the following frequencies: (a) 2.5 Hz (b) 00 Hz (c) 40 khz (a) Periodic time, T = = 0.4 s f 2.5 (b) Periodic
2. 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
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Circuits & Electronics Spring 2006
Massachusetts Institute of Technology Department of Electrical Engineering and omputer Science 6.002 ircuits & Electronics Spring 2006 Problem Set #9 Issued 4/12/06 Due 4/19/06 Exercise 9.1: Determine
Name 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
Mathematics 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
JUST THE MATHS SLIDES NUMBER 3.5. TRIGONOMETRY 5 (Trigonometric identities & wave-forms) A.J.Hobson
JUST THE MATHS SLIDES NUMBER 3.5 TRIGONOMETRY 5 (Trigonometric identities & wave-forms by A.J.Hobson 3.5.1 Trigonometric identities 3.5. Amplitude, wave-length, frequency and phase-angle UNIT 3.5 - TRIGONOMETRY
Exploring Graphs of Periodic Functions
8.2 Eploring Graphs of Periodic Functions GOAL Investigate the characteristics of the graphs of sine and cosine functions. EXPLORE the Math Carissa and Benjamin created a spinner. The glued graph paper
This exam contains 9 problems. CHECK THAT YOU HAVE A COMPLETE EXAM.
Math 126 Final Examination Winter 2012 Your Name Your Signature Student ID # Quiz Section Professor s Name TA s Name This exam contains 9 problems. CHECK THAT YOU HAVE A COMPLETE EXAM. This exam is closed
Math 148 Exam III Practice Problems
Math 48 Exam III Practice Problems This review should not be used as your sole source for preparation for the exam. You should also re-work all examples given in lecture, all homework problems, all lab
6.1 - Introduction to Periodic Functions
6.1 - Introduction to Periodic Functions Periodic Functions: Period, Midline, and Amplitude In general: A function f is periodic if its values repeat at regular intervals. Graphically, this means that
Math 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
PREREQUISITE/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
Precalculus ~ 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
Digital Image Processing COSC 6380/4393
Digital Image Processing COSC 6380/4393 Lecture 10 Feb 14 th, 2019 Pranav Mantini Slides from Dr. Shishir K Shah and S. Narasimhan Time and Frequency example : g(t) = sin(2π f t) + (1/3)sin(2π (3f) t)
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.
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. 1 1 1 Give the exact value of each expression.
Chapter 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.
GRAPHING TRIGONOMETRIC FUNCTIONS
GRAPHING TRIGONOMETRIC FUNCTIONS Section.6B Precalculus PreAP/Dual, Revised 7 viet.dang@humbleisd.net 8//8 : AM.6B: Graphing Trig Functions REVIEW OF GRAPHS 8//8 : AM.6B: Graphing Trig Functions A. Equation:
Unit 5 Investigating Trigonometry Graphs
Mathematics IV Frameworks Student Edition Unit 5 Investigating Trigonometry Graphs 1 st Edition Table of Contents INTRODUCTION:... 3 What s Your Temperature? Learning Task... Error! Bookmark not defined.
Chapter 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
Lesson 8.3: The Graphs of Sinusoidal Functions, page 536
. The graph of sin x repeats itself after it passes through 360 or π. 3. e.g. The graph is symmetrical along the x-axis, with the axis of symmetry being at 90 and 70, respectively. The graph is rotationally
First, frequency is being used in terms of radians per second which is often called "j*w0". The relationship is as such.
*=============EULER_Spectrum_Format================================== There appears to be several different styles of format for spectrum analysis. Perhaps the most precise format will translate according
How to Graph Trigonometric Functions
How to Graph Trigonometric Functions This handout includes instructions for graphing processes of basic, amplitude shifts, horizontal shifts, and vertical shifts of trigonometric functions. The Unit Circle
Sinusoidal Applications
Sinusoidal Applications A package of 5 activities Problems dealing with graphing and determining the equations of sinusoidal functions for real world situations Fractal image generated by MathWiz Created
Alternating voltages and currents
Alternating voltages and currents Introduction - Electricity is produced by generators at power stations and then distributed by a vast network of transmission lines (called the National Grid system) to
7.3 The Unit Circle Finding Trig Functions Using The Unit Circle Defining Sine and Cosine Functions from the Unit Circle
7.3 The Unit Circle Finding Trig Functions Using The Unit Circle For any angle t, we can label the intersection of the terminal side and the unit circle as by its coordinates,(x,y).the coordinates x and
Verifying Trigonometric Identities
25 PART I: Solutions to Odd-Numbered Exercises and Practice Tests a 27. sina =- ==> a = c. sin A = 20 sin 28 ~ 9.39 c B = 90 -A = 62 b cosa=- ==~ b=c.cosa~ 7.66 c 29. a = ~/c 2 - b 2 = -~/2.542-6.22 ~
Unit 7 Trigonometric Identities and Equations 7.1 Exploring Equivalent Trig Functions
Unit 7 Trigonometric Identities and Equations 7.1 Exploring Equivalent Trig Functions When we look at the graphs of sine, cosine, tangent and their reciprocals, it is clear that there will be points where
Trigonometric Equations
Chapter Three Trigonometric Equations Solving Simple Trigonometric Equations Algebraically Solving Complicated Trigonometric Equations Algebraically Graphs of Sine and Cosine Functions Solving Trigonometric
PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE)
Theory Class XI TARGET : JEE Main/Adv PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) MATHEMATICS Trigonometry SHARING IS CARING!! Want to Thank me? Share this Assignment with your friends and show
Investigating the Sine Function
Grade level: 9-12 Investigating the Sine Function by Marco A. Gonzalez Activity overview In this activity, students will use their Nspire handhelds to discover the different attributes of the graph of
Chapter 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.,
Graphs of other Trigonometric Functions
Graphs of other Trigonometric Functions Now we will look at other types of graphs: secant. tan x, cot x, csc x, sec x. We will start with the cosecant and y csc x In order to draw this graph we will first