4 4 graphing sine and cosine
Download
Skip this Video
Download Presentation
4-4 Graphing Sine and Cosine

Loading in 2 Seconds...

play fullscreen
1 / 18

4-4 Graphing Sine and Cosine - PowerPoint PPT Presentation


  • 158 Views
  • Uploaded on

4-4 Graphing Sine and Cosine. Chapter 4 Graphs of Trigonometric Functions. Warm-up. Find the exact value of each expression. sin 315 ° cot 510 °. 6-3 Objective: Use the graphs of sine and cosine (sinusoidal) functions 6-4 Objectives:

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '4-4 Graphing Sine and Cosine' - gaston


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
4 4 graphing sine and cosine

4-4 Graphing Sine and Cosine

Chapter 4

Graphs of Trigonometric Functions

warm up
Warm-up

Find the exact value of each expression.

  • sin 315°
  • cot 510°
slide3
6-3 Objective: Use the graphs of sine and cosine (sinusoidal) functions
  • 6-4 Objectives:
    • Find amplitude and period for sine and cosine functions, and
    • Write equations of sine and cosine functions given the amplitude and period.
    • Graph transformations of the sine and cosine functions
recreate the sine graph
Recreate the sine graph.
  • Domain and Range
  • x- and y-intercepts
  • symmetry
recreate the cosine graph
Recreate the cosine graph.
  • Domain and Range
  • x- and y-intercepts
  • symmetry
key concepts transformations of sine and cosine functions
KeyConcepts: Transformations of Sine and Cosine Functions

For y = a sin (bx + c) + d and y = a cos (bx + c) + d,

Amplitude (half the distance between the maximum and the minimum values of the function or half the height of the wave) = |a|

example 1
Example 1
  • Describe how the graphs of

f(x) = sin x and g(x) = 2.5 sin x

are related. Then find the amplitude of g(x). Sketch two periods of both functions.

example 2 reflections
Example 2 Reflections
  • Describe how f(x) = cos x and g(x) = -2cos x are related. Then find the amplitude of g(x). Sketch two periods of both functions.
key concepts transformations of sine and cosine functions1
KeyConcepts: Transformations of Sine and Cosine Functions

For y = a sin (bx + c) + d and y = a cos (bx + c) + d,

Period (distance between any two sets of repeating points on the graph) =

example 3
Example 3
  • Describe how the graphs of f(x) = cos x and g(x) = cos are related. Then find the period of g(x). Sketch at least one period of both functions.
key concepts transformations of sine and cosine functions2
KeyConcepts: Transformations of Sine and Cosine Functions

For y = a sin (bx + c) + d and y = a cos (bx + c) + d,

Frequency (the number of cycles the function completes in a one unit interval) =

(note that it is the reciprocal of the period or )

example 4
Example 4

A bass tuba can hit a note with a frequency

of 50 cycles per second (50 hertz) and

an amplitude of 0.75.

Write an equation for a

cosine function that

can be used to

model the initial

behavior of

the sound

wave associated

with the note.

key concepts transformations of sine and cosine functions3
KeyConcepts: Transformations of Sine and Cosine Functions

For y = a sin (bx + c) + d and y = a cos (bx + c) + d,

Phase shift (the difference between the horizontal position of the function and that of an otherwise similar function) =

example 5
Example 5
  • State the amplitude, period, frequency, and phase shift of . Then graph two periods of the function.
key concepts transformations of sine and cosine functions4
KeyConcepts: Transformations of Sine and Cosine Functions

For y = a sin (bx + c) + d and y = a cos (bx + c) + d,

Vertical shift (the average of the maximum and minimum of the function) = d

(Note the horizontal axis—the midline–is y = d)

example 6
Example 6
  • State the amplitude, period, frequency, phase shift, and vertical shift of y = sin (x + π) + 1. Then graph two periods of the function.
assignment
Assignment

P. 264, 1, 3, 9, 15, 17, 19.

ad