Trigonometry Examples

$135 \cdot \frac{π}{180}$

Step 1

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

$135 \cdot \frac{π}{180 °} \cdot \frac{π}{180 °}$ radians

Step 2

Cancel the common factor of $45$ .

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Step 2.1

Factor $45$ out of $135 \cdot \frac{π}{180}$ .

$45 (3 \cdot \frac{π}{180}) \cdot \frac{π}{180}$ radians

Step 2.2

Factor $45$ out of $180$ .

$45 (3 \cdot \frac{π}{180}) \cdot \frac{π}{45 (4)}$ radians

Step 2.3

Cancel the common factor.

$45 (3 \cdot \frac{π}{180}) \cdot \frac{π}{45 \cdot 4}$ radians

Step 2.4

Rewrite the expression.

$3 \cdot \frac{π}{180} \cdot \frac{π}{4}$ radians

Step 3

Combine $3$ and $\frac{π}{180}$ .

$\frac{3 π}{180} \cdot \frac{π}{4}$ radians

Step 4

Multiply $\frac{3 π}{180}$ by $\frac{π}{4}$ .

$\frac{3 π π}{180 \cdot 4}$ radians

Step 5

Raise $π$ to the power of $1$ .

$\frac{3 (π π)}{180 \cdot 4}$ radians

Step 6

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

$\frac{3 π^{1 + 1}}{180 \cdot 4}$ radians

Step 7

Simplify the expression.

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Step 7.1

Add $1$ and $1$ .

$\frac{3 π^{2}}{180 \cdot 4}$ radians

Step 7.2

Multiply $180$ by $4$ .

$\frac{3 π^{2}}{720}$ radians

Step 8

Cancel the common factor of $3$ and $720$ .

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Step 8.1

Factor $3$ out of $3 π^{2}$ .

$\frac{3 (π^{2})}{720}$ radians

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $720$ .

$\frac{3 π^{2}}{3 \cdot 240}$ radians

Step 8.2.2

Cancel the common factor.

$\frac{3 π^{2}}{3 \cdot 240}$ radians

Step 8.2.3

Rewrite the expression.

$\frac{π^{2}}{240}$ radians