Precalculus Examples

$\arccos (\cos (\frac{17 π}{6}))$

Step 1

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

$\arccos (\cos (\frac{5 π}{6}))$

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 second quadrant.

$\arccos (- \cos (\frac{π}{6}))$

Step 3

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$\arccos (- \frac{\sqrt{3}}{2})$

Step 4

The exact value of $\arccos (- \frac{\sqrt{3}}{2})$ is $\frac{5 π}{6}$ .

$\frac{5 π}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 π}{6}$

Decimal Form:

$2.61799387 \dots$