Graphing the Cosine Function

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Show your work for each problem.

1.
What is the value of ?
1. a)
2. b)
3. c)
4. d)
2.
What is the period of ?
1. a)
2. b)
3. c)
4. d)
3.
What is the amplitude of ?
4.
What is the value of ?
5.
At what x-value does first cross the x-axis (starting from )?
1. a)
2. b)
3. c)
4. d)
6.
What is the amplitude of ?
7.
What is the period of ?
1. a)
2. b)
3. c)
4. d)
8.
What is the period of ? Express your answer as a fraction of (e.g., enter "pi/2" for ).
9.
The graph of is shifted in which direction compared to ?
1. a)Right by
2. b)Down by
3. c)Left by
4. d)Up by
10.
What is the maximum value of ?
11.
Find the amplitude, period, and midline of .
12.
Describe all transformations of compared to .
13.
Find the equation of a cosine function with amplitude 2, period , and phase shift to the right.
14.
Which equation represents a cosine function with a maximum at and minimum at ?
1. a)
2. b)
3. c)
4. d)
15.
A ferris wheel has a diameter of 40 meters and its center is 25 meters above the ground. It takes 2 minutes for one full rotation. Write a cosine function for a rider's height above the ground, where is in minutes and the rider starts at the top.
16.
What is the minimum value of ?