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Post1330_section5o2_fri - Section 5.2 Graphs of the Sine...

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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 > 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:
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Section 5.2 – Graphs of the Sine and Cosine Functions 2 Now let’s talk about the graphs of the sine and cosine functions. Recall: sin( 2 ) sin θ π θ = and cos( 2 ) cos θ π θ = This means that after going around the unit circle once ( 2 π radians), both functions repeat. So the period of both sine and cosine is 2 π . Hence, we can find the whole number line wrapped around the unit circle.
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