Trigonometry Examples

$\cos (\frac{π}{2} - x)$

Step 1

Apply the difference 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 $1$ .

$0 + 1 \sin (x)$

Step 2.1.4

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

$0 + \sin (x)$

Step 2.2

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

$\sin (x)$