$\"\"$

The function is $\"\"$ .

If $\"\"$ be the point on the unit circle that corresponds to $\"\"$ , then $\"\"$ is the point on the unit circle that corresponds to $\"\"$ .

Thus, $\"\"$ . $\"\"$

Suppose that there exists a number $\"\"$ , $\"\"$ , for which $\"\"$ for all $\"\"$ .

Then, if $\"\"$ , then $\"\"$ .

But this means that $\"\"$ is a multiple of $\"\"$ .

Since no multiple of $\"\"$ exists in the interval $\"\"$ , this is a contradiction.

Therefore, the period of $\"\"$ is $\"\"$ .

$\"\"$

The period of $\"\"$ is $\"\"$ .