Trigonometry Examples

$\sin (x + π)$

Step 1

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

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

Step 2

Remove parentheses.

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

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. Make the expression negative because cosine is negative in the second quadrant.

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

Step 3.2

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

$\sin (x) (- 1 \cdot 1) + \cos (x) \sin (π)$

Step 3.3

Multiply $- 1$ by $1$ .

$\sin (x) \cdot - 1 + \cos (x) \sin (π)$

Step 3.4

Move $- 1$ to the left of $\sin (x)$ .

$- 1 \cdot \sin (x) + \cos (x) \sin (π)$

Step 3.5

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

$- \sin (x) + \cos (x) \sin (π)$

Step 3.6

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

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

Step 3.7

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

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

Step 3.8

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

$- \sin (x) + 0$

Step 4

Add $- \sin (x)$ and $0$ .

$- \sin (x)$