Determine the corresponding ordered pair of the point on the unit circle for the following angle: -5 pi over 3

Question

Choices are ;

 

(1/2, sqrt 3/2)

 

(1/2, - sqrt 3/2)

 

(-1/2, sqrt 3/2)

 

(-1/2, - sqrt 3/2)

Answer 1

Make sure you have your unit circle ready!

Dealing with negatives is just about starting at 0 and going clockwise.  Though the easy way to look at it is to find the positive version of your angle on the unit circle, then find the reflection over the y-axis.  This will be your unit circle coordinate.

 

5π/3 is in quadrant IV.  Reflect over the y-axis into quadrant I, which puts you at π/3, which is equivalent to -5π/3.  This makes the point (1/2, sqrt 3/2).