The function is .

 is differentiable at all values of  because it is a trigonometric function.

Critical number :

A critical number of a function  is a number  in the domain of  such that either  or    does not exist.

Therefore, solutions of  are the critical numbers.

Differentiate  on each side with respect to .

Equate  to zero.

 and 

 and .

The general solution of  is , where  is an integer.

The general solution of  is , where  is an integer.

Consider .

.

The general solution is .

Consider 

The general solution is .

The critical numbers are all numbers of the form  (  is an integer).

The critical numbers are all numbers of the form  (  is an integer).