Trigonometry Examples

$165 \cdot \frac{π}{180}$

Step 1

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

$165 \cdot \frac{π}{180 °} \cdot \frac{π}{180 °}$ radians

Step 2

Cancel the common factor of $15$ .

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Step 2.1

Factor $15$ out of $165 \cdot \frac{π}{180}$ .

$15 (11 \cdot \frac{π}{180}) \cdot \frac{π}{180}$ radians

Step 2.2

Factor $15$ out of $180$ .

$15 (11 \cdot \frac{π}{180}) \cdot \frac{π}{15 (12)}$ radians

Step 2.3

Cancel the common factor.

$15 (11 \cdot \frac{π}{180}) \cdot \frac{π}{15 \cdot 12}$ radians

Step 2.4

Rewrite the expression.

$11 \cdot \frac{π}{180} \cdot \frac{π}{12}$ radians

Step 3

Combine $11$ and $\frac{π}{180}$ .

$\frac{11 π}{180} \cdot \frac{π}{12}$ radians

Step 4

Multiply $\frac{11 π}{180}$ by $\frac{π}{12}$ .

$\frac{11 π π}{180 \cdot 12}$ radians

Step 5

Raise $π$ to the power of $1$ .

$\frac{11 (π π)}{180 \cdot 12}$ radians

Step 6

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

$\frac{11 π^{1 + 1}}{180 \cdot 12}$ radians

Step 7

Add $1$ and $1$ .

$\frac{11 π^{2}}{180 \cdot 12}$ radians

Step 8

Multiply $180$ by $12$ .

$\frac{11 π^{2}}{2160}$ radians