Chapter 4, Problem 6RE

Solution

To find: The quadrant of the terminal side of the angle $112°$ and convert it to radians.

The terminal side of the angle $112°$ lies in the second quadrant and its value in radians is $\frac{28\pi }{45}$ .

Given information: The given angle is $112°$ .

Calculation:

The value of both $\pi$ radians and $180°$ is a straight line. The conversion factor of $\frac{\pi }{180°}$ is used to convert degrees into radians.

Conversion of $112°$ degrees into radian.

  $112°\times \frac{\pi }{180°}=\frac{28\pi }{45}$

Each quadrant on the Cartesian plane has a range of $90°$ . The first quadrant has the angles from $0°-90°$, the second quadrant has the angles from $90°-180°$, the third quadrant has the angles from $180°-270°$, and the fourth quadrant has the angles from $270°-360°$. So, the angle $112°$ lies in the second quadrant.

Thus, the terminal side of the angle $112°$ lies in the second quadrant and its value in degrees is $\frac{28\pi }{45}$ .