Precalculus Examples

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

Step 1

To convert degrees to radians, multiply by $\frac{π}{180 °}$ , since a full circle is $360 °$ or $2 π$ radians.

Step 2

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

$- \frac{π}{6} \cdot \frac{π}{180}$ radians

Step 3

Multiply $- \frac{π}{6} \cdot \frac{π}{180}$ .

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Step 3.1

Multiply $\frac{π}{180}$ by $\frac{π}{6}$ .

$- \frac{π π}{180 \cdot 6}$ radians

Step 3.2

Raise $π$ to the power of $1$ .

$- \frac{π π}{180 \cdot 6}$ radians

Step 3.3

Raise $π$ to the power of $1$ .

$- \frac{π π}{180 \cdot 6}$ radians

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{π^{1 + 1}}{180 \cdot 6}$ radians

Step 3.5

Add $1$ and $1$ .

$- \frac{π^{2}}{180 \cdot 6}$ radians

Step 3.6

Multiply $180$ by $6$ .

$- \frac{π^{2}}{1080}$ radians