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Unformatted text preview: Section 5.2 Graphs of the Sine and Cosine Functions 1 Section 5.2 Graphs of the Sine and Cosine Functions A Periodic Function and Its Period A nonconstant function f is said to be periodic if there is a number p &gt; 0 such that f ( x + p ) = f ( x ) for all x in the domain of f . The smallest such number p is called the period of f . The graphs of periodic functions display patterns that repeat themselves at regular intervals. Amplitude Let f be a periodic function and let m and M denote, respectively, the minimum and maximum values of the function. Then the amplitude of f is the number 2 m M- . In other words the amplitude is half the height. Example 1: Section 5.2 Graphs of the Sine and Cosine Functions 2 Now lets talk about the graphs of the sine and cosine functions. Recall: sin( 2 ) sin + = and cos( 2 ) cos + = This means that after going around the unit circle once ( 2 radians), both functions repeat. So the period of both sine and cosine is 2 . Hence, we can find the whole...
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This note was uploaded on 02/20/2012 for the course MATH 1330 taught by Professor Staff during the Fall '08 term at University of Houston.
- Fall '08