Trigonometry Examples

$\cos (\frac{π}{2} + θ)$

Step 1

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

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

Step 2

Remove parentheses.

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

Step 3

Simplify each term.

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Step 3.1

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

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

Step 3.2

Multiply $\cos (θ)$ by $0$ .

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

Step 3.3

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

$0 - \sin (θ) \cdot 1$

Step 3.4

Multiply $- 1$ by $1$ .

$0 - \sin (θ)$

Step 4

Subtract $\sin (θ)$ from $0$ .

$- \sin (θ)$