Trigonometry Examples

$\sin (x - π)$

Step 1

Use the difference 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.

Tap for more steps...

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 $- \cos (x) \cdot 0$ .

Tap for more steps...

Step 3.8.1

Multiply $0$ by $- 1$ .

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

Step 3.8.2

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

$- \sin (x) + 0$

Step 4

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

$- \sin (x)$