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Trigonometry 1.1:
Finding Patterns in Periodic Functions
Student Name:
Definitions
Period
The period of a function is the length of one repeating pattern in the graph. In the graph below the pattern repeats approximately every 6 units.
The period of a function can be calculated by using  , where B is in the form of  . For example, in the function  , B would be 3. In most of the functions in this assignment  .
Amplitude
The amplitude of a function is a measure of the "height" of the curve. The amplitude is calculated by taking half the difference between the maximum and minimum function values.
In the graph below, the maximum function value is approximately 3 and the minimum is about -.5. The amplitude equals  or 1.75.
Practice Problems
Graph the following trigonometric functions and record the period and amplitude of each function.
The first problem has been graphed for you. To continue, copy the input command, change the function to your problem, and press 
 .
Describe any patterns you may see among the period and amplitude calculations. Do your "patterns" hold true if the functions change? For example, what about sin, cos, tan, csc, sec, and cot of  ? What if the function is 2 Sin[x]?
    
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