Precalculus Examples

$y = \arctan (\tan (- \frac{5 π}{6}))$

Step 1

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

$y = \arctan (\tan (\frac{7 π}{6}))$

Step 2

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

$y = \arctan (\tan (\frac{π}{6}))$

Step 3

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

$y = \arctan (\frac{\sqrt{3}}{3})$

Step 4

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

$y = \frac{π}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{π}{6}$

Decimal Form:

$y = 0.52359877 \dots$