Notes 4-7
Upcoming SlideShare
Loading in...5
×
 

Notes 4-7

on

  • 1,190 views

Scale-Change Images of Circular Functions

Scale-Change Images of Circular Functions

Statistics

Views

Total Views
1,190
Views on SlideShare
879
Embed Views
311

Actions

Likes
0
Downloads
5
Comments
0

3 Embeds 311

http://mrlambmath.wikispaces.com 275
https://mrlambmath.wikispaces.com 35
http://webcache.googleusercontent.com 1

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

Notes 4-7 Notes 4-7 Presentation Transcript

  • Section 4-7 Scale-Change Images of Circular Functions
  • Warm-up Graph each of these equations on the same axes for -π ≤ θ ≤ π y = sin x y = 3sin x y = sin 2x y = 3sin2x All together:
  • Recall that a periodic function has a value such that f(x + p) = f(x), where p is the period of the function. The trig functions (sine, cosine, and tangent) are all periodic, as they begin to trace the same output values after a certain amount of input values.
  • Sine Wave: The graph of the sine or cosine function over a composite or translations and scale changes Amplitude: Half the distance between the maximum and minimum output values
  • Example 1 What is the period of sine? Cosine? Tangent? Sine and cosine both have periods of 2π. Tangent has a period of π.
  • Example 2 a. Graph y = sin x and y = 5sin x for -2π ≤ x ≤ 2π. b. What are the amplitude and period of these graphs? For y = sin x, the amplitude is 1 and the period is 2π For the second graph, the amplitude is 5 and the period stays the same.
  • Example 2 c. Graph y = cos x and y = cos 6x for -2π ≤ x ≤ 2π. d. What are the amplitude and period of these graphs? For y = cos x, the amplitude is 1 and the period is 2π For the second graph, the amplitude is 1 and the period is π/3.
  • Theorem for Amplitude and Period For the functions ⎛ x⎞ ⎛ x⎞ and y = bsin⎜ ⎟ y = bcos⎜ ⎟ ⎝ a⎠ ⎝ a⎠ amplitude is|b| and period is 2π|a| ***NOTICE: a is in the denominator, so be careful when working with it!!!
  • Frequency: The number of cycles the curve completes per unit of the independent variable Found by taking reciprocal of the period
  • Example 3 Consider the graph for y = sin2x 1 4 Give the period, amplitude, and frequency Period = π Amplitude = 1 4 a = 12 1 Frequency = π
  • Example 4 Suppose a tuning fork vibrates with a frequency of 440 cycles per second. If the vibration displaces air molecules by a maximum of .2mm, give a possible equation for the sound wave produced. y = .2sin(880πx )
  • Homework p. 275 # 1 - 18