The derivative and primitive function rules in Calculus are applicable to Trigonometric Functions. Several rules are listed below:

Simple differentiation and integration of trigonometric functions:

General formula of the derivatives of trigonometric functions:

General formula of the primitives of trigonometric functions:

### Examples

1. Differentiate .

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2. Find the exact value of the gradient of the tangent to the curve at the point where .

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3. Evaluate .

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4. Find the area enclosed between the curve , the *x*-axis, in the domain of and .

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The graph above shows the intended area of focus. Remember that, from integration principles, the area below the *x*-axis would be zero, so we need to use two separate integrations. First, we evaluate the area between and , then we evaluate the negative area between and .

Therefore,

5. Find the primitive function of using substitution.

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