Trigonometry Examples

$- \frac{4 π}{3}$

Step 1

Convert the radian measure to degrees.

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Step 1.1

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

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

Step 1.2

Cancel the common factor of $π$ .

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Step 1.2.1

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

$\frac{- 4 π}{3} \cdot \frac{180}{π}$

Step 1.2.2

Factor $π$ out of $- 4 π$ .

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

Step 1.2.3

Cancel the common factor.

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

Step 1.2.4

Rewrite the expression.

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

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $180$ .

$\frac{- 4}{3} \cdot (3 (60))$

Step 1.3.2

Cancel the common factor.

$\frac{- 4}{3} \cdot (3 \cdot 60)$

Step 1.3.3

Rewrite the expression.

$- 4 \cdot 60$

Step 1.4

Multiply $- 4$ by $60$ .

$- 240$

Step 1.5

Convert to a decimal.

$- 240 °$

Step 2

For angles smaller than $0 °$ , add $360 °$ to the angle until the angle is larger than $0 °$ .

$120$

Step 3

The angle is in the second quadrant.

Quadrant $2$

Step 4