Algebra Examples

$\arccos (- \frac{1}{2})$

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 $\arccos (- \frac{1}{2})$ is $\frac{2 π}{3}$ .

$\frac{2 π}{3} \cdot \frac{π}{180}$ radians

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $2 π$ .

$\frac{2 (π)}{3} \cdot \frac{π}{180}$ radians

Step 3.2

Factor $2$ out of $180$ .

$\frac{2 (π)}{3} \cdot \frac{π}{2 (90)}$ radians

Step 3.3

Cancel the common factor.

$\frac{2 π}{3} \cdot \frac{π}{2 \cdot 90}$ radians

Step 3.4

Rewrite the expression.

$\frac{π}{3} \cdot \frac{π}{90}$ radians

Step 4

Multiply $\frac{π}{3}$ by $\frac{π}{90}$ .

$\frac{π π}{3 \cdot 90}$ radians

Step 5

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

$\frac{π^{1 + 1}}{3 \cdot 90}$ radians

Step 6

Add $1$ and $1$ .

$\frac{π^{2}}{3 \cdot 90}$ radians

Step 7

Multiply $3$ by $90$ .

$\frac{π^{2}}{270}$ radians