Trigonometry Examples

$\arctan (\tan (- \frac{π}{6}))$

Step 1

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

$\arctan (\tan (\frac{11 π}{6}))$

Step 2

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

$\arctan (- \tan (\frac{π}{6}))$

Step 3

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

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

Step 4

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

$- \frac{π}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{6}$

Decimal Form:

$- 0.52359877 \dots$