Trigonometry Examples

$46 (\frac{π}{180})$

Step 1

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

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $46 (\frac{π}{180})$ .

$2 (23 (\frac{π}{180})) \cdot \frac{π}{180}$ radians

Step 2.2

Factor $2$ out of $180$ .

$2 (23 (\frac{π}{180})) \cdot \frac{π}{2 (90)}$ radians

Step 2.3

Cancel the common factor.

$2 (23 (\frac{π}{180})) \cdot \frac{π}{2 \cdot 90}$ radians

Step 2.4

Rewrite the expression.

$23 (\frac{π}{180}) \cdot \frac{π}{90}$ radians

Step 3

Combine $23$ and $\frac{π}{180}$ .

$\frac{23 π}{180} \cdot \frac{π}{90}$ radians

Step 4

Multiply $\frac{23 π}{180}$ by $\frac{π}{90}$ .

$\frac{23 π π}{180 \cdot 90}$ radians

Step 5

Raise $π$ to the power of $1$ .

$\frac{23 (π π)}{180 \cdot 90}$ radians

Step 6

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

$\frac{23 π^{1 + 1}}{180 \cdot 90}$ radians

Step 7

Add $1$ and $1$ .

$\frac{23 π^{2}}{180 \cdot 90}$ radians

Step 8

Multiply $180$ by $90$ .

$\frac{23 π^{2}}{16200}$ radians