Precalculus Examples

$y = \arctan (\tan (\frac{2 π}{3}))$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

$y = \arctan (- \tan (\frac{π}{3}))$

Step 2

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

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

Step 3

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

$y = - \frac{π}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{π}{3}$

Decimal Form:

$y = - 1.04719755 \dots$