Trigonometry Examples

$\sin (π + x)$

Step 1

Use the sum formula for sine to simplify the expression. The formula states that $\sin (A + B) = \sin (A) \cos (B) + \cos (A) \sin (B)$ .

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

Step 2

Remove parentheses.

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

Step 3

Simplify each term.

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Step 3.1

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

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

Step 3.2

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

$0 \cos (x) + \cos (π) \sin (x)$

Step 3.3

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

$0 + \cos (π) \sin (x)$

Step 3.4

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.

$0 - \cos (0) \sin (x)$

Step 3.5

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

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

Step 3.6

Multiply $- 1$ by $1$ .

$0 - 1 \sin (x)$

Step 3.7

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

$0 - \sin (x)$

Step 4

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

$- \sin (x)$