The Sine Function

Warm up

Press the play button or move the slider.

What is the x-value of the red point?

Tick your answer here

What is the y-value of the red point?

Tick your answer here
Tracing the red points results in the graph of . This sine function relates an angle measure in radians to the y-value of a point on the unit circle.

What type of function is the sine function?

Tick your answer here

Transforming Sine Functions

Move the sliders.

How does changing the slider for a affect the graph of this sine function?

What happens to the graph when a is negative?

How does changing the slider for b affect the graph of this sine function?

Key Concept (Take Note!)

For the periodic function , where , , and is an angle in radians:
  • The amplitude of the function is .
  • The function has cycles between 0 and .
  • The period of the function is .

Which function would have an amplitude of 4?

Tick your answer here

Which function would have a period of pi?

Tick your answer here

Sketching a Sine Function

  1. Draw an x-axis from 0 to the period of the function. Divide the period into 4 pieces.
  2. Draw a y-axis from the amplitude to the opposite of the amplitude.
  3. Use a five-point summary to sketch the graph of a sine function:
zero-max-zero-min-zero if a is positive.  zero-min-zero-max-zero if a is negative.

Sketch the graph of .

Write an equation for the sine function shown above.

Exercise!

pg. 848 - 849 #15 - 30 all, 47, 48