Trigonometry Examples

$\sin (x - \frac{π}{2}) = - \cos (x)$

Step 1

Start on the left side.

$\sin (x - \frac{π}{2})$

Step 2

Apply the difference of angles identity.

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

Step 3

Simplify the expression.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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

Step 3.1.2

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

$0 - \cos (x) \sin (\frac{π}{2})$

Step 3.1.3

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

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

Step 3.1.4

Multiply $- 1$ by $1$ .

$0 - \cos (x)$

Step 3.2

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

$- \cos (x)$

Step 4

Because the two sides have been shown to be equivalent, the equation is an identity.

$\sin (x - \frac{π}{2}) = - \cos (x)$ is an identity