00:01
So if a point is on the unit circle, then that x is the cosine of the angle, and y is the sine of the angle.
00:14
And to get tangent, we would just take y over x, or sine over cosine.
00:22
So let's look at the first problem.
00:23
We're given y, and that's 3 4ths.
00:26
So the equation of the unit circle is x squared plus y squared equals 1.
00:39
So x squared is 1 minus y squared.
00:42
If y is 3 4ths, then x squared is 1 minus 3 4ths squared, or 1 minus 9 over 16, which is 16 over 16 minus 9 over 16, and that's going to give me 7 over 16.
01:03
So x is plus or minus the square root of 7 over 16, which is going to be rad 7 over 4.
01:15
Because i'm in quadrant 1, i know that x has to be positive rad 7 over 4.
01:23
So the sine of my angle is just the y value...