Find the Quadrant of the Angle (18pi)/5

$\frac{18 π}{5}$

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.

$(\frac{18 π}{5}) \cdot \frac{180 °}{π}$

Cancel the common factor of $π$ .

Factor $π$ out of $18 π$ .

$\frac{π \cdot 18}{5} \cdot \frac{180}{π}$

Cancel the common factor.

$\frac{π \cdot 18}{5} \cdot \frac{180}{π}$

Rewrite the expression.

$\frac{18}{5} \cdot 180$

Cancel the common factor of $5$ .

Factor $5$ out of $180$ .

$\frac{18}{5} \cdot (5 (36))$

Cancel the common factor.

$\frac{18}{5} \cdot (5 \cdot 36)$

Rewrite the expression.

$18 \cdot 36$

Multiply $18$ by $36$ .

$648$

Convert to a decimal.

$648 °$

Step 2

For angles greater than $360 °$ , subtract $360 °$ from the angle until the angle is less than $360 °$ .

$288$

Step 3

The angle is in the fourth quadrant.

Quadrant $4$

Step 4