Trigonometry Examples

$\cos (270 ° - θ)$

Step 1

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

$\cos (270 °) \cdot \cos (θ) + \sin (270 °) \cdot \sin (θ)$

Step 2

Remove parentheses.

$\cos (270 °) \cdot \cos (θ) + \sin (270 °) \cdot \sin (θ)$

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 third quadrant.

$- \cos (90) \cdot \cos (θ) + \sin (270 °) \cdot \sin (θ)$

Step 3.2

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

$- 0 \cdot \cos (θ) + \sin (270 °) \cdot \sin (θ)$

Step 3.3

Multiply $- 1$ by $0$ .

$0 \cdot \cos (θ) + \sin (270 °) \cdot \sin (θ)$

Step 3.4

Multiply $0$ by $\cos (θ)$ .

$0 + \sin (270 °) \cdot \sin (θ)$

Step 3.5

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.

$0 - \sin (90) \cdot \sin (θ)$

Step 3.6

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

$0 - 1 \cdot 1 \cdot \sin (θ)$

Step 3.7

Multiply $- 1$ by $1$ .

$0 - 1 \cdot \sin (θ)$

Step 3.8

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

$0 - \sin (θ)$

Step 4

Subtract $\sin (θ)$ from $0$ .

$- \sin (θ)$