Trigonometry Examples

$\sin (270 - x)$

Step 1

Apply the difference of angles identity.

$\sin (270) \cos (x) - \cos (270) \sin (x)$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

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

$- \sin (90) \cos (x) - \cos (270) \sin (x)$

Step 2.1.2

The exact value of $\sin (90)$ is $1$ .

$- 1 \cdot 1 \cos (x) - \cos (270) \sin (x)$

Step 2.1.3

Multiply $- 1$ by $1$ .

$- 1 \cos (x) - \cos (270) \sin (x)$

Step 2.1.4

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

$- \cos (x) - \cos (270) \sin (x)$

Step 2.1.5

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 third quadrant.

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

Step 2.1.6

The exact value of $\cos (90)$ is $0$ .

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

Step 2.1.7

Multiply $- - 0$ .

Tap for more steps...

Step 2.1.7.1

Multiply $- 1$ by $0$ .

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

Step 2.1.7.2

Multiply $- 1$ by $0$ .

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

Step 2.1.8

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

$- \cos (x) + 0$

Step 2.2

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

$- \cos (x)$