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Period of a Function If the values of a function are the same for each given interval, it is said to be “periodic.” The interval is the period of the function.

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(When converted to this form, “n” will be an even number; not an x-intercept since ½ pi is added) The x-intercepts of the sin function are always integer multiples of π Is it the correct form for a max or a min?

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The x-intercepts for sin(x) are... 5π5π3π3π4π4π 1 all multiples of pi. The maximum values of y = 1 are...at the even ½ pi values. The minimum values of y = -1 are...at the odd ½ pi values.

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Formulas given to us in the book:

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Example 6 Determine whether the graph represents y = sin x, y = cos x, or neither. The x-intercepts are not at integer values of pi; this eliminates the possibility of it being a sine function. The maximum value is an even integer of π ; the minimum values are an odd integer of π. This is an indication of a cosine function. The x-intercepts can be rewritten as: which is another indication of a cosine function. The graph represents y = cos x,

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HW: Page 363

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November 29, 2012 Period and Amplitude of the Sine and Cosine Functions Warm-up: Finish Sine and Cosine Function Activity (15 minutes) HW 4.5: Pg. 328-329.

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