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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,
HW: Page 363HW: Page 363