Period of a Period of a FunctionFunction

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.

2

228

29

4

(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 . . .

5π3π 4π

1

-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 6Example 6Determine 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.

2

2216

217

8

2

2214

215

7

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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