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Critical number :

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

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$\"\"$

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The function is $\"\"$ .

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

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Therefore, solutions of $\"\"$ are the critical numbers.

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Differentiate $\"\"$ on each side with respect to $\"\"$ .

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$\"\"$

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Equate $\"\"$ to zero.

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$\"\"$

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$\"\"$

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The general solution of $\"\"$ is $\"\"$ , where $\"\"$ is an integer.

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Consider $\"\"$ .

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$\"\"$

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The general solution is $\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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The general solution is $\"\"$ .

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The critical numbers are all numbers of the form $\"\"$ or $\"\"$ , Where $\"\"$ is an integer.

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The critical numbers are all numbers of the form $\"\"$ or $\"\"$ .

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Where $\"\"$ is an integer.