Determine the corresponding ordered pair of the point on the unit circle for the following angle: -13 pi over 6

Question

Determine the corresponding ordered pair of the point on the unit circle for the following angle: -13 pi over 6

Answer 1

There are 2 pi radians in a circle.  -13 pi/6 is (-2 pi) - (pi/6), so the angle is really just -pi/6 (-30^o) (or +11 pi/6 (330^o)).

 

cos(-pi/6) = x/1 = x = (√3)/2,  where the 1 is the radius of the unit circle.

 

sin(-pi/6) = y/1 = y = -1/2

 

The coordinates of the point on the unit circle are ((√3)/2, -1/2)