What is ?
We need to find before we can find its negative.
is the 60 degrees in a 30-60-90 triangle. That means the opposite side is (not the longest or shortest side), and the hypotenuse is 2.
is in the first quadrant, so the sign is already correct.
Except we want sine of the negative angle, which gives the opposite result. That means:
We need to find cosine of positive . Again.
is in the second quadrant, and its corresponding acute angle is .
The x-coordinate (and thus cosine) is negative in the second quadrant.
Now we have to find cosine of the negative angle. However, cosine of a negative angle is the same as cosine of the positive angle.
This time, we don't need to find the positive corresponding acute angle.
(i.e. 90 degrees) has coordinates (0, 1) on the unit circle. That means .
Negative is the same as positive , so it's no surprise that sin is negative.
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?
before we can find its negative.
is the 60 degrees in a 30-60-90 triangle. That means the opposite side is 
(not the longest or shortest side), and the hypotenuse is 2.
?
. Again.
.
?
(i.e. 90 degrees) has coordinates (0, 1) on the unit circle. That means 
.
is the same as positive 
, so it's no surprise that sin is negative.