Trigonometry Examples

$θ = \frac{8 π}{9}$

Step 1

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

$θ + \frac{8 π}{9 °} \cdot \frac{π}{180 °}$ radians

Step 2

Cancel the common factor of $4$ .

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Step 2.1

Factor $4$ out of $8 π$ .

$θ + \frac{4 (2 π)}{9} \cdot \frac{π}{180}$ radians

Step 2.2

Factor $4$ out of $180$ .

$θ + \frac{4 (2 π)}{9} \cdot \frac{π}{4 (45)}$ radians

Step 2.3

Cancel the common factor.

$θ + \frac{4 (2 π)}{9} \cdot \frac{π}{4 \cdot 45}$ radians

Step 2.4

Rewrite the expression.

$θ + \frac{2 π}{9} \cdot \frac{π}{45}$ radians

Step 3

Multiply $\frac{2 π}{9}$ by $\frac{π}{45}$ .

$θ + \frac{2 π π}{9 \cdot 45}$ radians

Step 4

Raise $π$ to the power of $1$ .

$θ + \frac{2 (π π)}{9 \cdot 45}$ radians

Step 5

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

$θ + \frac{2 π^{1 + 1}}{9 \cdot 45}$ radians

Step 6

Add $1$ and $1$ .

$θ + \frac{2 π^{2}}{9 \cdot 45}$ radians

Step 7

Multiply $9$ by $45$ .

$θ + \frac{2 π^{2}}{405}$ radians