Trigonometry Examples

$\arctan (\tan (\frac{5 π}{6}))$

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.

$\arctan (- \tan (\frac{π}{6}))$

Step 2

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

$\arctan (- \frac{\sqrt{3}}{3})$

Step 3

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

$- \frac{π}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{6}$

Decimal Form:

$- 0.52359877 \dots$