Precalculus Examples

$\cos (225) - \cos (30)$

Step 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.

$- \cos (45) - \cos (30)$

Step 2

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

$- \frac{\sqrt{2}}{2} - \cos (30)$

Step 3

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$- \frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2}$

Decimal Form:

$- 1.57313218 \dots$