Question

An angle in standard position measures −5π3 radians. In which quadrant does the terminal side of this angle lie?

Answer 1

Answer:

The terminal side of this angle lies in the first quadrant.

Solution:

Given, an angle in standard position measures −5π/3 radians.  

We need to find in which quadrant does the terminal side of this angle lie.

First let us convert -5π/3 radians into degrees.

$\text { Now, } \frac{-5 \pi}{3} \text { radians }=\frac{-5 \pi}{3} \times \frac{180}{\pi} \text { degrees }$

$=\frac{-5}{3} \times 180 \text { degrees }$

= -5 x 60 degrees = -300 degrees

Here, -300 represents that terminal side is rotating in anti clock wise direction. So now to find the positive angle.

Positive angle = 360 – 300 = 60 degrees

We know that, 0 degrees < 60 degrees < 90 degrees

Hence, the terminal side of this angle lies in the first quadrant.