Determine the corresponding ordered pair of the point on the unit circle for the following angle: 16 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

Hey sheila,

 

This is another problem where we are given an angle that is greater than 1 full revolution (2pi), so we can subtract multiples of 2pi from the 16pi/3 until we are in the range of 0-2pi.

 

16pi/3 - 2pi = 16pi/3 - 6pi/3 = 10pi/3

 

10pi/3 - 2pi = 10pi/3 - 6pi/3 = 4pi/3

 

4pi/3 is within the range of 0-2pi, so we can find the quadrant that this corresponds to (in this case 4pi/3 would be in the 3rd quad).

 

We can use a 30/60/90 reference triangle (the sides and angles for this reference triangle along with the 45/45/90 reference triangle make up the entire the unit circle!).