Trigonometry Examples

$\sin (90 ° - θ) = \cos (θ)$

Step 1

Start on the left side.

$\sin (90 ° - θ)$

Step 2

Apply the difference of angles identity.

$\sin (90 °) \cos (θ) - \cos (90 °) \sin (θ)$

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 $\sin (90 °)$ is $1$ .

$1 \cos (θ) - \cos (90 °) \sin (θ)$

Step 3.1.2

Multiply $\cos (θ)$ by $1$ .

$\cos (θ) - \cos (90 °) \sin (θ)$

Step 3.1.3

The exact value of $\cos (90 °)$ is $0$ .

$\cos (θ) - 0 \sin (θ)$

Step 3.1.4

Multiply $- 1$ by $0$ .

$\cos (θ) + 0 \sin (θ)$

Step 3.1.5

Multiply $0$ by $\sin (θ)$ .

$\cos (θ) + 0$

Step 3.2

Add $\cos (θ)$ and $0$ .

$\cos (θ)$

Step 4

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

$\sin (90 ° - θ) = \cos (θ)$ is an identity