Trigonometry Examples

$\cos (x + \frac{π}{2})$

Step 1

Use the sum formula for cosine to simplify the expression. The formula states that $\cos (A + B) = - (\cos (A) \cos (B) + \sin (A) \sin (B))$ .

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

Step 2

Remove parentheses.

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

Step 3

Simplify each term.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Multiply $- 1$ by $1$ .

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

Step 3.5

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

$0 - \sin (x)$

Step 4

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

$- \sin (x)$