I need help finding values through the unit circle?

The first problem is a lot more simple than you'd think. Imagine a 90 degree angle (right angle). The two legs of the triangle will be equal on the unit circle (the x length and the y length). well, what's sin equal to? y/x, correct? well, 1/1 = 1. so sin 90 = 1

As for cot -270, you need to break this up. First off, when degrees is negative, you go in the opposite direction (clockwise). So since 270 is just 90 x 3, go 3 right angles then stop. You'll notice, in fact, this is exactly the same angle as 90 degrees. Now we have to consider what cot actually is. Well we know that tangent is sin/cos, and cot is the reverse, so cot is cos/sin. Therefore, you look at what cos 90 is. So look at the unit circle, notice once more that its directly on the y axis, so therefore x = 0. So cos 90 = 0. We already know from above that sin 90 is 1. so 0/1 = 0.

A slightly quicker way of looking at is knowing already from previous knowledge that tan 90 is undefined, so therefore its some fraction with zero as the denominator. Since we flipped it to make it cot, you flip the fraction so zero is the numerator, and that will just make the fraction end up being 0.

I know that was a lot to swallow, but I hope it made sense!

sin of 90 is located at 0,1 on a unit circle

sin is the y value of this coordinate which is 1

sine of 90 is 1

cot-270 would be going around the unit circle clockwise which would give you 90degrees or the coordinate (0,1)

cot is cos over sin so 0/1 is 0