Trigonometry Examples

$\sin (\frac{π}{2} - x)$

Step 1

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

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

Step 2

Remove parentheses.

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

Step 3

Simplify each term.

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Step 3.1

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

$1 \cos (x) - \cos (\frac{π}{2}) \sin (x)$

Step 3.2

Multiply $\cos (x)$ by $1$ .

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

Step 3.3

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

$\cos (x) - 0 \sin (x)$

Step 3.4

Multiply $- 1$ by $0$ .

$\cos (x) + 0 \sin (x)$

Step 3.5

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

$\cos (x) + 0$

Step 4

Add $\cos (x)$ and $0$ .

$\cos (x)$