00:01
So we're given sine of theta is equal to 5 13ths and our theta is between 90 and 180.
00:07
So what this tells us is we're in quadrant 2.
00:12
So let's draw our triangle.
00:16
So sine is opposite over hypotenuse.
00:22
So we know our opposite side is 5, our hypotenuse is 13, and we want to find this x value.
00:29
So that's 5 squared plus x squared is equal to 13 squared.
00:36
So x is equal to square root of 13 squared minus 25, which you should get is equal to 12.
00:47
So our x equals 12, but remember we're in the second quadrant, so this x value is going to be negative.
01:02
All right, so now we have a angle formula for sine that's equal to plus or minus square root of 1 minus cosine x over 2.
01:15
So we need to find what's cosine of.
01:21
So remember cosine of x is equal to the adjacent over hypotenuse.
01:28
So that means we have negative 12 over 13.
01:33
So now let's plug this in.
01:35
So you get this is equal to plus or minus square root of 1 minus negative 12 over 13 over 2.
01:45
1 minus negative over 13, so i'll be adding that.
01:50
So our numerator is going to be 13 plus 12...