Chapter 4, Problem 5RE

Solution

To find: The quadrant of the terminal side of the angle $78°$ and convert it to radians.

The terminal side of the angle $78°$ lies in the first quadrant and its value in radians is $\frac{13\pi }{30}$ .

Given information: The given angle is $78°$ .

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 $78°$ degrees into radian.

  $78°\times \frac{\pi }{180°}=\frac{13\pi }{30}$

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 $78°$ lies in the first quadrant.

Thus, the terminal side of the angle $78°$ lies in the first quadrant and its value in degrees is $\frac{13\pi }{30}$ .