Find the Quadrant of the Angle -(15pi)/17

$- \frac{15 π}{17}$

Step 1

Convert the radian measure to degrees.

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

$(- \frac{15 π}{17}) \cdot \frac{180 °}{π}$

Cancel the common factor of $π$ .

Move the leading negative in $- \frac{15 π}{17}$ into the numerator.

$\frac{- 15 π}{17} \cdot \frac{180}{π}$

Factor $π$ out of $- 15 π$ .

$\frac{π \cdot - 15}{17} \cdot \frac{180}{π}$

Cancel the common factor.

$\frac{π \cdot - 15}{17} \cdot \frac{180}{π}$

Rewrite the expression.

$\frac{- 15}{17} \cdot 180$

Combine $\frac{- 15}{17}$ and $180$ .

$\frac{- 15 \cdot 180}{17}$

Simplify the expression.

Multiply $- 15$ by $180$ .

$\frac{- 2700}{17}$

Move the negative in front of the fraction.

$- \frac{2700}{17}$

Convert to a decimal.

$- 158.82352941 °$

Step 2

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

$201.17647058$

Step 3

The angle is in the third quadrant.

Quadrant $3$

Step 4