CP Algebra II
Name: __________________________
Graphing Sine and Cosine
5/7/14
Warm-Up:
1.
On the Unit Circle, we define the following trigonometric ratios using x, y, and r. Fill in the ratios.
a. sin  

2.
b. cos 
Evaluate with exact values:
a. sin 90Þ

c. tan  

b. cos


4

c. tan225Þ

d. sin 270Þ

Remember: A Unit Circle has a radius of:______________
A point on the Unit Circle can be defined as (x, y), or:______________________
Sine and Cosine are defined using a unit circle, and thus are called _____________________ functions.
A Periodic Function has y-values that repeat at regular intervals. One complete pattern is a
_______________, and the horizontal length of one cycle is a __________________.
Example #1: Determine the period of the function pictured.
Example #2: The pedals on a bicycle rotate as the bike is being ridden. The height of a pedal is a function
of time, as shown in the picture.
Period: __________ seconds
Time
0
.5
1
1.5
2
2.5
3
(s)
Height
(in.)
Graph the function. Let the horizontal axis represent the time t and the vertical axis represent the
height h in inches that the pedal is from the ground.
Example #3: Using a similar idea, we can graph just the values of the sine function as we work our way
around the unit circle. Our points on the graph will be ( , sin  ) , or in other words
(angle, y - coordinate on the unit circle) . Some angles from the unit circle are listed in the table below to
guide your work.

0˚

30˚
45˚
60˚
90˚
120˚
180˚
210˚
270˚
300˚
360˚
sin 


The _______________________________ of the graph of a sine or cosine function equals half the difference
between the maximum and minimum values of the function.
Domain:
Period:
Range:
Amplitude:
Homework:
1.
Fill in the table below using your unit circle. Remember, for the Cosine graph our points will be
(angle, x-coordinate on the unit circle).
0˚

30˚
45˚
60˚
90˚
120˚
180˚
210˚
270˚
300˚
360˚
cos

 2.
Graph the Cosine Function using the points from the table.
3.
For the Cosine Graph above, identify the domain, range, amplitude, and period.
Domain:
Range:
Amplitude:
Period:
Verbally describe the transformation on each cosine graph. (Hint: y  acos(  h)  k )
4.
a.
y  cos  2
b.
y  5cos



c.

y  cos  50 o
d.

y  3cos