Question

In which quadrant does the terminal side of the angle 387° lie?

Answer 1

We'll reduce the angle to an angle smaller than 360 degress first. So 387 = 360 * 1 + 27 It is obvious that 387 lies in the same quadrant as 27. But 27 lies between 0 and 90. Hence it lies in the first quadrant.

Answer 2

To evaluate the quadrant we first reduce the angle to a smaller angle than 360°:

387°=360°+27°

so 387° lies in the same quadrant as 27°

The angle 27° lies between 0° and 90°, so its terminal side lies in the 1st quadrant.