Trigonometry Examples

$- \frac{4 π}{3}$

Step 1

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

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

Step 2

Cancel the common factor of $4$ .

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Step 2.1

Move the leading negative in $- \frac{4 π}{3}$ into the numerator.

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

Step 2.2

Factor $4$ out of $- 4 π$ .

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

Step 2.3

Factor $4$ out of $180$ .

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

Step 2.4

Cancel the common factor.

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

Step 2.5

Rewrite the expression.

$\frac{- π}{3} \cdot \frac{π}{45}$ radians

Step 3

Multiply $\frac{- π}{3}$ by $\frac{π}{45}$ .

$\frac{- π π}{3 \cdot 45}$ radians

Step 4

Raise $π$ to the power of $1$ .

$\frac{- (π π)}{3 \cdot 45}$ radians

Step 5

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

$\frac{- π^{1 + 1}}{3 \cdot 45}$ radians

Step 6

Add $1$ and $1$ .

$\frac{- π^{2}}{3 \cdot 45}$ radians

Step 7

Multiply $3$ by $45$ .

$\frac{- π^{2}}{135}$ radians

Step 8

Move the negative in front of the fraction.

$- \frac{π^{2}}{135}$ radians