# Math Assignment Help With Periodic Function

## 9.5 Periodic function:

A function f(*x*) is called periodic if there is a non-zero number p such that f(*x*+p) is defined and f(*x*+p) = f(*x*) for all values of *x *in the domain of f(*x)*. The number p is called the period of f(*x*).

The function sin*x* has periods 2p, 4p,6p,....since sin (*x*+2p), sin (*x*+4p), sin (*x*+6p),....all equal sin *x.* However, 2p is the least period or the period of sin*x*.

The function cosx has periods 2p, 4p, 6p, ....... since cos(x+2p), cos(x+4p), cos(x+6p), ....... all equal cos*x*. Here also 2p is the period, i.e., the least period or the period of cos x.

The period of tan*x* is p.

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