Chapter 6.4, Problem 102AYU

To determine

To calculate: the term period as it relates to graph of the sinusoidal function.

Explanation of Solution

The period of function $f(x)$ is $T$ if $f(x+T)=f(x)$ for every $x$ in domain of $f$ . The natural period for $\sin x$ and $\cos x$ is $T=2\pi$ , as $\sin (x+2\pi )=\sin x$ for any $x$ .

In graph, the distance between the two same regions of sinusoidal wave. The highest point of sine or cosine wave forms are $2\pi$ apart.