This problem is totally about understanding our unit circle and or our right triangles and knowing how to use them. So sine of 45 if I think about my unit circle, 4545 right triangle means my two sides are equivalent in lengths. Now using my a ^2 + b ^2 = C ^2 I can find the hypotenuse. The hypotenuse being the side opposite the right angle. So 1 ^2 + 1 ^2 = C ^2. So we get C being sqrt 2. Now in a unit circle, that hypotenuse has to be one. So what we're going to do is we're going to divide every side by sqrt 2, because if I do one side, I have to do all of them. And sqrt 2 / sqrt 2 is now one. We rationalize the rest of this. So we're going to multiply by root 2 over root 2 to rationalize. So we get sqrt 2 / 2 for the two sides. Remember the sine is how far up I've gone. So if we do an ordered triplet, we go over to the right root 2 / 2, we go up root 2 / 2, and then the Y divided by the X is 1 and that's cosine, sine and tangent. So our first part of the sine 45 is just going to be root 2 / 2. We're going to do the same thing for cosine of 60. And I was actually going to put them both on the same triangle or on the circle, but I think it's a little too busy. So I'm going to do my own over here when I have sinus 60. This is my 60°. That makes this a 306090. Now we could think about this as being a 6060 sixty equilateral if we wanted to. If we did that, what we would do is we'd make the sides each two so that when I cut the base in half, we got one. Now we're going to find that last side. So a ^2 + b ^2 = C ^2 again. So this time we have 1 ^2 plus our b ^2 because we know the hypotenuse this time. So b ^2 = 4 -, 1 or B is sqrt 3. Now, just like before, we want the hypotenuse to be one. So we're going to take this entire thing and divide everything through by two because 2 / 2 is 1. So we can see that we've gone over 1/2. We've gone up root 3 / 2. And then if I divide my sine divided by cosine or my y / X, I'd get root 3. So when it says what's cosine of 60 we can see that that's 1/2 and when we multiply these two we get sqrt 2 / 4.