1. 13-4 – The Sine Function
Mr. Kohls

2. Graphing the Sine Function

3. Highlights of the Sine Function
The sine function, Ѳ matches the measure of an angle in standard position with the y-coordinate of a point on the unit circle.
Within one cycle of the function the graph will “zero” by touching the x axis three times ( ); reach a minimum value of -1 at and a maximum value of 1 at

4. The Sine Function Use the graph of the sine function.
a What is the value of y= sin for = 180°?
The value of the function at = 180° is 0.
b. For what other value(s) of from 0° to 360° does the graph of sin have the same value as for = 180°?
When y = 0, = 0° and 360°.

5. The Sine Function
Estimate each value from the graph. Check your estimate with a calculator.
a. sin 3
The sine function reaches its median value of 0 at The value of the function at 3 is slightly more than 0, or about 0.1.
sin 3 =    Use a calculator to check your estimate.

6. The Sine Function
(continued)
b. sin 2
The sine function reaches its maximum value of 1 at , so sin = 1. 2
sin = 1 Use a calculator to check your estimate. 2

7. The Sine Function
Use the graph. Find the value(s) of each of the following.
1. the period
2. the amplitude

8. Graphing the Sine Function
Sketch one cycle of each sine curve. Assume a>0
Amplitude = 2
Period = π

9. Graphing the Sine Function
Sketch one cycle of each sine curve. Assume a>0
Amplitude = 4
Period = π 2