Trigonometry Examples

$\cos (\frac{π}{2} + x)$

Step 1

Apply the sum of angles identity $\cos (x + y) = \cos (x) \cos (y) - \sin (x) \sin (y)$ .

$\cos (\frac{π}{2}) \cos (x) - \sin (\frac{π}{2}) \sin (x)$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$0 \cos (x) - \sin (\frac{π}{2}) \sin (x)$

Step 2.1.2

Multiply $0$ by $\cos (x)$ .

$0 - \sin (\frac{π}{2}) \sin (x)$

Step 2.1.3

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$0 - 1 \cdot 1 \sin (x)$

Step 2.1.4

Multiply $- 1$ by $1$ .

$0 - 1 \sin (x)$

Step 2.1.5

Rewrite $- 1 \sin (x)$ as $- \sin (x)$ .

$0 - \sin (x)$

Step 2.2

Subtract $\sin (x)$ from $0$ .

$- \sin (x)$