GDC Set up Ensure that your calculator is in degree mode and that you know how to adjust the v-window of your graphs before doing these trigonometry graphs.

Slides:

Advertisements

Similar presentations

GRAPHS OF OTHER TRIG FUNCTIONS

Advertisements

Reading and Drawing Sine and Cosine Graphs

Trig Graphs Investigate the effects of 2sin(x), 2cos(x), 2tan(x)

Graphs of the Sine, Cosine, & Tangent Functions Objectives: 1. Graph the sine, cosine, & tangent functions. 2. State all the values in the domain of a.

A brief journey into Section 4.5a HW: p , 4, 5, 9, 13, 25, 27.

The arc length spanned, or cut off, by an angle is shown next:

4.5 Graphs of Sine and Cosine Functions

Copyright © 2009 Pearson Education, Inc. CHAPTER 6: The Trigonometric Functions 6.1The Trigonometric Functions of Acute Angles 6.2Applications of Right.

Trig – Section 4 Graphing Sine and Cosine Objectives: To graph sine and cosine curves To find amplitude, period and phase shifts.

Graphing Sine and Cosine. Graphing Calculator Mode— Radians Par Simul Window— –X min = -1 –X max = 2  –X scale =  /2 Window— –Y min = -3 –Y max = 3.

Graphing Sine and Cosine. Video Graphing Calculator Mode— Radians Par Simul Window— –X min = -1 –X max = 2  –X scale =  /2 Window— –Y min = -3 –Y max.

Evaluating Sine & Cosine and and Tangent (Section 7.4)

We need to sketch the graph of y = 3sin(5t+90)

5.6 Transformations of the Sine and Cosine Graphs Wed Nov 12 Do Now Use the sine and cosine values of 0, pi/2, pi, 3pi/2 and 2pi to sketch the graph of.

Section Frequency of Sine and Cosine Graphs.

Objectives Graphs of Sine and Cosine

MAT 204 SP Graphs of the Sine and Cosine Functions 7.8 Phase shift; Sinusoidal Curve Fitting In these sections, we will study the following topics:

Graphs Transformation of Sine and Cosine

Aim: What is the transformation of trig functions? Do Now: HW: Handout Graph: y = 2 sin x and y = 2 sin x + 1, 0 ≤ x ≤ 2π on the same set of axes.

Graphs of Trig Functions

MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions Section 6 – Graphs of Transformed Sine and Cosine Functions.

Nat 5 Creation of BASIC Trig Graphs Graphs of the form y = a sin xo

Starter a 6 c A 53° 84° 1.Use Law of Sines to calculate side c of the triangle. 2.Use the Law of Cosines to calculate side a of the triangle. 3.Now find.

The World’s Largest Ferris Wheel

Trigonometric Functions

January 24 th copyright2009merrydavidson. y = cos x.

Locating Points on a Circle Sine Cosine Tangent. Coordinates Systems Review There are 3 types of coordinate systems which we will use: Absolute Incremental.

The Wave Function Heart beat Electrical Many wave shapes, whether occurring as sound, light, water or electrical waves, can be described mathematically.

Period and Amplitude Changes

Trigonometric Functions

The Trig Graphs Build-A-Graph Day (5.5). POD #1 Complete these limit statements. For limit statements, go to the graphs, not the unit circle. For which.

Section Recall Then you applied these to several oblique triangles and developed the law of sines and the law of cosines.

4.7 Inverse Trig Functions. By the end of today, we will learn about….. Inverse Sine Function Inverse Cosine and Tangent Functions Composing Trigonometric.

Periodic Functions. A periodic function is a function f such the f(x) = f(x + np) for every real number x in the domain of f, every integer n, and some.

More Trig – Graphing Trig Functions

Chapter 14 Day 8 Graphing Sin and Cos. A periodic function is a function whose output values repeat at regular intervals. Such a function is said to have.

Algebra II Honors Problem of the Day Homework: p a,b,g,3c,d,5,9,13,29,41,43 After watching the video graph y = cos t and y = sin t. graphing the.

Section 4.5 Graphs of Sine and Cosine Functions. The Graph of y=sin x.

Periodic Function Review

Graphing Trig Functions Review Whiteboard Activity.

Aims: To know the relationship between the graphs and notation of cosine, sine and tan, with secant, cosecant and cotangent. To be able to state the domain.

Trigonometry Ratios.

7.4 Trigonometry What you’ll learn:

Writing Equations of Trigonometric Graphs Dr. Shildneck Fall.

Chapter 2 Trigonometric Functions of Real Numbers Section 2.3 Trigonometric Graphs.

Chapter 6 Section 6.4 Translations of the Graphs of Sine and Cosine Functions.

Warm up Use the Pythagorean identity to determine if the point (.623,.377) is on the circumference of the unit circle Using Pythagorean identity, solve.

UNIT 6: GRAPHING TRIG AND LAWS Final Exam Review.

Notes Over 14.1 Graph Sine, Cosine, and Tangent Functions.

1. Be able to write down the period and amplitude from a graph 2. Be able to state the period and amplitude from an equation 3. Be able to write down equation.

8-3 Trigonometry Part 2: Inverse Trigonometric Functions.

4.5 Graphs of Sine and Cosine Functions Page in PreCalc book

Chapter 6 Section 6.3 Graphs of Sine and Cosine Functions.

Trigonometry Section 7.4 Find the sine and cosine of special angles. Consider the angles 20 o and 160 o Note: sin 20 o = sin160 o and cos 20 o = -cos 160.

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle Common Core Standards for Chapter 6 The arc in.

Warm Up Evaluate Find the measure of the reference angle for each given angle that would be on the unit circle ° 5.

Section 2.5 Transformations.

Graphing Trigonometry Functions

Work on worksheet with 8 multiple choice questions.

Writing Equations of Trigonometric Graphs

TRIGONOMETRIC GRAPHS.

Graphs of Sine and Cosine

Notes Over 6.4 Graph Sine, Cosine Functions.

Frequency and Phase Shifts

4.2 – Translations of the Graphs of the Sine and Cosine Functions

Writing Trig Functions

Section 4.5 Graphs of Sine and Cosine Functions

Graphing: Sine and Cosine

Graphs of Sine and Cosine Sinusoids

Trigonometric Ratios Geometry.

Presentation transcript:

GDC Set up Ensure that your calculator is in degree mode and that you know how to adjust the v-window of your graphs before doing these trigonometry graphs.

Amplitude of sine graphs

Amplitude of cosine graphs

Amplitude of a trig graph A graph of y=sin(x) is shown below. This graph has an amplitude of 1. The graph of y=2sin(x) has an amplitude of 2. The graph of y=3sin(x) has an amplitude of 3. This pattern will also work with cosine graphs.

Amplitude of trig. graphs You will have discovered from previous slides that multiplying a trig graph by a number stretches the graph. The multiplying factor of the graph is known as the graph’s amplitude.

Amplitude of trig graphs 1 Find the amplitude of the graph below.

Amplitude of trig graphs 2 Find the value of a in f(x)=asinx, graphed below.

Period of sine graphs

Period of cosine graphs

Period of a trig graph A graph of y=cos(x) is shown below. This graph has an period of 360 - the length it takes to make a complete wave. The graph of y=cos(2x) has an period of 180. The graph of y=cos(3x) has an period of 120.

Period of trig. graphs You will have discovered from previous slides that multiplying the x by a constant increases the number of ‘waves’ the graph does. This is called the period - the time it takes to complete one cycle.

Period of trig. graphs Find the period of each of these graphs.

Period of trig graphs 1 Find the period of the graph below.

Vertical shift of trig. graphs

Vertical shift of trig. graphs

Shift of a trig graph A graph of y=cos(x) is shown below. Look at where this graph starts (0,1). The graph of y=cos(x)+2 has a shift of 2. The graph of y=cos(x)-3 has a shift of -3 This pattern will also work with sine graphs.

Vertical shift of trig. graphs You will have discovered from previous slides that adding a constant onto the trig graph will move the graph up, or down if the constant is negative. Write down the y-coordinate where the graph crosses the y-axis for each of these functions.

Putting it all together Amplitude Vertical shift Calculates the period This is the general expression for a trig. graph which has been transformed. If you are trying to find the values of the letters then find a first, b second and c last. This format also works for cosine and tangent graphs.

Finding a, b and c

Finding a, b and c

Finding a, b and c

Finding a, b and c