Precalculus Examples

$\cos (- \frac{2}{3} \cdot π)$

Step 1

Combine $π$ and $\frac{2}{3}$ .

$\cos (- \frac{π \cdot 2}{3})$

Step 2

Move $2$ to the left of $π$ .

$\cos (- \frac{2 \cdot π}{3})$

Step 3

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\cos (\frac{4 π}{3})$

Step 4

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.

$- \cos (\frac{π}{3})$

Step 5

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$- \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$