Determine the corresponding ordered pair of the point on the unit circle for the following angle: 17 pi over 6

Question

Choices are ;

 

(- sqrt 3/2, 1/2)

 

(sqrt 3/2, 1/2)

 

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

 

( sqrt 3/2, -1/2)

Answer 1

The answer is (- sqrt 3/2, 1/2).

It will help to look at a Unit Circle chart. A quick google search should bring up an image.

17pi/6 is what you started with. As a mixed fraction, it looks like "2 and 5/6 * pi" (which can also be written as 2 and 5pi/6)

Now, look at your unit circle. Count off the 2 pi counter clockwise. 2 pi takes you 360 degrees (full circle), so you are back where you started. Now, continue going counter clockwise and count of 5pi/6. (You can also think of this as counting off another pi and then adding back 1/6pi)

That is a position on the chart in Quadrant 2. The associated coordinate is (- sqrt 3/2, 1/2).