Precalculus Examples

$\arccos (\cos (- \frac{2 π}{3}))$

Step 1

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

$\arccos (\cos (\frac{4 π}{3}))$

Step 2

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.

$\arccos (- \cos (\frac{π}{3}))$

Step 3

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

$\arccos (- \frac{1}{2})$

Step 4

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

$\frac{2 π}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 π}{3}$

Decimal Form:

$2.09439510 \dots$