Trigonometry Examples

\sin (90 - θ)

$\sin (90 - θ)$

Step 1

Apply the difference of angles identity.

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

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

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

\sin (90)

$\sin (90)$ is

1

$1$ .

1 \cos (θ) - \cos (90) \sin (θ)

$1 \cos (θ) - \cos (90) \sin (θ)$

Step 2.1.2

Multiply

\cos (θ)

$\cos (θ)$ by

1

$1$ .

\cos (θ) - \cos (90) \sin (θ)

$\cos (θ) - \cos (90) \sin (θ)$

Step 2.1.3

The exact value of

\cos (90)

$\cos (90)$ is

0

$0$ .

\cos (θ) - 0 \sin (θ)

$\cos (θ) - 0 \sin (θ)$

Step 2.1.4

Multiply

- 1

$- 1$ by

0

$0$ .

\cos (θ) + 0 \sin (θ)

$\cos (θ) + 0 \sin (θ)$

Step 2.1.5

Multiply

0

$0$ by

\sin (θ)

$\sin (θ)$ .

\cos (θ) + 0

$\cos (θ) + 0$

\cos (θ) + 0

$\cos (θ) + 0$

Step 2.2

Add

\cos (θ)

$\cos (θ)$ and

0

$0$ .

\cos (θ)

$\cos (θ)$

\cos (θ)

$\cos (θ)$

\sin (90 - θ)

$\sin (90 - θ)$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$