Trigonometry Examples

$\cos (270 - x)$

Step 1

Apply the difference of angles identity $\cos (x - y) = \cos (x) \cos (y) + \sin (x) \sin (y)$ .

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

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

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

Step 2.1.2

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

$- 0 \cos (x) + \sin (270) \sin (x)$

Step 2.1.3

Multiply $- 1$ by $0$ .

$0 \cos (x) + \sin (270) \sin (x)$

Step 2.1.4

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

$0 + \sin (270) \sin (x)$

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 sine is negative in the third quadrant.

$0 - \sin (90) \sin (x)$

Step 2.1.6

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

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

Step 2.1.7

Multiply $- 1$ by $1$ .

$0 - 1 \sin (x)$

Step 2.1.8

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

$0 - \sin (x)$

Step 2.2

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

$- \sin (x)$