Trigonometry Examples

$120 ° \cdot \frac{π}{180}$

Step 1

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

$120 ° \cdot \frac{π}{180} \cdot \frac{π}{180 °}$ radians

Step 2

Cancel the common factor of $60$ .

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Step 2.1

Factor $60$ out of $120 \cdot \frac{π}{180}$ .

$60 (2 \cdot \frac{π}{180}) \cdot \frac{π}{180}$ radians

Step 2.2

Factor $60$ out of $180$ .

$60 (2 \cdot \frac{π}{180}) \cdot \frac{π}{60 (3)}$ radians

Step 2.3

Cancel the common factor.

$60 (2 \cdot \frac{π}{180}) \cdot \frac{π}{60 \cdot 3}$ radians

Step 2.4

Rewrite the expression.

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

Step 3

Combine $2$ and $\frac{π}{180}$ .

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

Step 4

Multiply $\frac{2 π}{180}$ by $\frac{π}{3}$ .

$\frac{2 π π}{180 \cdot 3}$ radians

Step 5

Raise $π$ to the power of $1$ .

$\frac{2 (π π)}{180 \cdot 3}$ radians

Step 6

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

$\frac{2 π^{1 + 1}}{180 \cdot 3}$ radians

Step 7

Simplify the expression.

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Step 7.1

Add $1$ and $1$ .

$\frac{2 π^{2}}{180 \cdot 3}$ radians

Step 7.2

Multiply $180$ by $3$ .

$\frac{2 π^{2}}{540}$ radians

Step 8

Cancel the common factor of $2$ and $540$ .

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Step 8.1

Factor $2$ out of $2 π^{2}$ .

$\frac{2 (π^{2})}{540}$ radians

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $540$ .

$\frac{2 π^{2}}{2 \cdot 270}$ radians

Step 8.2.2

Cancel the common factor.

$\frac{2 π^{2}}{2 \cdot 270}$ radians

Step 8.2.3

Rewrite the expression.

$\frac{π^{2}}{270}$ radians