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     ...
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 f...
Sine Wave: The graph of the sine or cosine
   function over a composite or translations and
   scale changes




Amplitude...
Example 1
What is the period of sine? Cosine? Tangent?


  Sine and cosine both have periods of 2π.
         Tangent has a...
Example 2
 a. Graph y = sin x and y = 5sin x for -2π ≤ x ≤ 2π.




 b. What are the amplitude and period of these
        ...
Example 2
 c. Graph y = cos x and y = cos 6x for -2π ≤ x ≤ 2π.




 d. What are the amplitude and period of these
        ...
Theorem for Amplitude and Period

                 For the functions
                    ⎛ x⎞                 ⎛ x⎞
       ...
Frequency:



The number of cycles the curve completes per
      unit of the independent variable


  Found by taking reci...
Example 3
    Consider the graph for y = sin2x
                               1
                               4

Give the...
Example 4
Suppose a tuning fork vibrates with a frequency of
 440 cycles per second. If the vibration displaces
   air mol...
Homework

 p. 275 # 1 - 18
Upcoming SlideShare
Loading in …5
×

Notes 4-7

1,046 views

Published on

Scale-Change Images of Circular Functions

Published in: Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,046
On SlideShare
0
From Embeds
0
Number of Embeds
338
Actions
Shares
0
Downloads
7
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Notes 4-7

  1. 1. Section 4-7 Scale-Change Images of Circular Functions
  2. 2. 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:
  3. 3. 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.
  4. 4. 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
  5. 5. Example 1 What is the period of sine? Cosine? Tangent? Sine and cosine both have periods of 2π. Tangent has a period of π.
  6. 6. 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.
  7. 7. 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.
  8. 8. 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!!!
  9. 9. Frequency: The number of cycles the curve completes per unit of the independent variable Found by taking reciprocal of the period
  10. 10. 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
  11. 11. 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 )
  12. 12. Homework p. 275 # 1 - 18

×