Download presentation

Presentation is loading. Please wait.

Published byLauren Sander Modified over 3 years ago

1
4.5 – Graphs of Sine and Cosine A function is periodic if f(x + np) = f(x) for every x in the domain of f, every integer n, and some positive number p (called the period).

2
4.5 – Graphs of Sine and Cosine xy 00 1 π0 −1 2π2π0 y = sin x −2π −π π 2π 3π 4π

3
Characteristics of the Sine Function 1)The domain is. 2)The range is [-1, 1]. 3)The period is. 4)The sine function is an odd function. It is symmetric with respect to the origin. sin (x) = -sin (x)

4
4.5 – Graphs of Sine and Cosine xy 01 0 π−1 0 2π2π1 y = cos x −2π −π π 2π 3π 4π

5
Characteristics of the Cosine Function 1)The domain is. 2)The range is [-1, 1]. 3)The period is. 4)The sine function is an even function. It is symmetric with respect to the y-axis. cos (x) = cos (-x)

6
4.5 – Graphs of Sine and Cosine −2π −π π 2π 3π 4π Graphing y = a sin x y = 2 sin x y = sin x ½

7
4.5 – Graphs of Sine and Cosine −2π −π π 2π 3π 4π Graphing y = sin bx y = sin 2x y = sin x ½

8
4.5 – Graphs of Sine and Cosine −2π −π π 2π 3π 4π Graphing y = sin(x − c) y = sin ( x + 2 ) y = sin x y = sin(x − π) π

9
4.5 – Graphs of Sine and Cosine Graphing y = sin(bx − c) 0 bx − c 2π c bx c + 2π starting pointending point

10
4.5 – Graphs of Sine and Cosine Graphing y = a sin(bx − c) 1.Find amplitude = | a | 2.Find period = 3.Find phase shift = 4.Find the interval on the x-axis. 5.Divide the interval into fourths to plot “key points”. 6.Graph one period. Extend if necessary.

11
4.5 – Graphs of Sine and Cosine Graph the equation y = 3 sin(2x − π) amplitude: period: phase shift: interval: 3 = π π2π2π

12
4.5 – Graphs of Sine and Cosine Graph the equation y = amplitude: period: p. s.: interval: 4π4π2π2π = 2π(2)= 4π = −π(2)= −2π [−2π, 2π] −2π 1 −1

13
4.5 – Graphs of Sine and Cosine −2π −π π 2π 3π 4π Graphing y = sin(x) + d y = sin ( x) + 2 y = sin x y = sin(x) − 1

14
4.5 – Graphs of Sine and Cosine Graph the equation y = sin(2x − π) + 2 amplitude: period: phase shift: interval: vertical shift: 1 = π up 2 units π2π2π

Similar presentations

OK

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

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

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on polynomials in maths what does median Best ppt on french revolution Ppt on fair and lovely Ppt on 2nd world war flags Ppt on polymers used in daily life Ppt on solar system for class 9 Ppt on technology vs science Ppt on chapter 3 drainage cap Ppt on crime file management system in java Ppt on interview skills training