Trigonometry Examples

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

Step 1

Simplify each term.

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Step 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 second quadrant.

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

Step 1.2

The exact value of

$\cos (0)$ is

$1$ .

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

Step 1.3

Multiply

$- 1$ by

$1$ .

$- 1 \cos (x) - \sin (π) \sin (x)$

Step 1.4

Rewrite

$- 1 \cos (x)$ as

$- \cos (x)$ .

$- \cos (x) - \sin (π) \sin (x)$

Step 1.5

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

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

Step 1.6

The exact value of

$\sin (0)$ is

$0$ .

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

Step 1.7

Multiply

$- 1$ by

$0$ .

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

Step 1.8

Multiply

$0$ by

$\sin (x)$ .

$- \cos (x) + 0$

Step 2

Add

$- \cos (x)$ and

$0$ .

$- \cos (x)$