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.

(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?

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.

Formulas given to us in the book:

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,

HW: Page 363