Find the Quadrant of the Angle (23pi)/8

$\frac{23 π}{8}$

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.

$(\frac{23 π}{8}) \cdot \frac{180 °}{π}$

Cancel the common factor of $π$ .

Factor $π$ out of $23 π$ .

$\frac{π \cdot 23}{8} \cdot \frac{180}{π}$

Cancel the common factor.

$\frac{π \cdot 23}{8} \cdot \frac{180}{π}$

Rewrite the expression.

$\frac{23}{8} \cdot 180$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{23}{4 (2)} \cdot 180$

Factor $4$ out of $180$ .

$\frac{23}{4 \cdot 2} \cdot (4 \cdot 45)$

Cancel the common factor.

$\frac{23}{4 \cdot 2} \cdot (4 \cdot 45)$

Rewrite the expression.

$\frac{23}{2} \cdot 45$

Combine $\frac{23}{2}$ and $45$ .

$\frac{23 \cdot 45}{2}$

Multiply $23$ by $45$ .

$\frac{1035}{2}$

Convert to a decimal.

$517.5 °$

Step 2

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

$157.5$

Step 3

The angle is in the second quadrant.

Quadrant $2$

Step 4