<h3>
Answer: 2 goes in the blank on the left; 3 goes in the blank on the right</h3>
In other words, (-1/2, sqrt(3)/2) is the point in question
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Explanation:
The angle 240 degrees is in quadrant 3, so we subtract 180 from this angle to get 240 - 180 = 60 which is the reference angle
Now refer to a 30-60-90 triangle template. Note how the side opposite the 30 degree angle is the shortest leg, which is half that of the hypotenuse. In this case, the hypotenuse is 1. Therefore the short leg is 1/2. This value is made negative due to the fact cosine is negative for quadrant 3. In other words, the x coordinate of the point on the unit circle is negative here.
The long leg is sqrt(3) times that of the short leg 1/2, so we end up with (1/2)*sqrt(3) = sqrt(3)/2, which is then made negative from the fact that y is negative in quadrant 3. Put another way, sine is negative in quadrant 3.
If you want to use trig functions rather than a 30-60-90 triangle template, then you would say
cos(60) = 1/2
sin(60) = sqrt(3)/2
Then make each value negative as you transition to quadrant 3
cos(240) = -1/2
sin(240) = -sqrt(3)/2
The point (-1/2, -sqrt(3)/2) is on the unit circle such that a 240 degree angle forms.
