Precalculus Examples

$\sin (π + θ)$

Step 1

Apply the sum of angles identity.

$\sin (π) \cos (θ) + \cos (π) \sin (θ)$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin (0) \cos (θ) + \cos (π) \sin (θ)$

Step 2.1.2

The exact value of $\sin (0)$ is $0$ .

$0 \cos (θ) + \cos (π) \sin (θ)$

Step 2.1.3

Multiply $0$ by $\cos (θ)$ .

$0 + \cos (π) \sin (θ)$

Step 2.1.4

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$0 - \cos (0) \sin (θ)$

Step 2.1.5

The exact value of $\cos (0)$ is $1$ .

$0 - 1 \cdot 1 \sin (θ)$

Step 2.1.6

Multiply $- 1$ by $1$ .

$0 - 1 \sin (θ)$

Step 2.1.7

Rewrite $- 1 \sin (θ)$ as $- \sin (θ)$ .

$0 - \sin (θ)$

Step 2.2

Subtract $\sin (θ)$ from $0$ .

$- \sin (θ)$