00:01
So we want to find all solutions in degrees for sine of 2 theta is equal to 1 half.
00:17
Well if you look at our unit circle, 1 half, if the sine is 1 half, that puts our y value on the unit circle at 1 half.
00:30
So our angles then are going to be this one here, as well as this one here, because both of these have a y value equal to 1 half.
00:44
And this first one, this is 90 degrees, so this is 40, no it's 30 degrees.
00:53
And this one here then is 180 degrees minus 30 degrees, so this is 150 degrees.
01:02
So that means that 2 theta is the inverse sine of 1 half, which is equal to 30 degrees and 150 degrees.
01:22
So that means that theta is going to be 15 degrees, or 75 degrees.
01:31
But we also get these answers when we add 360 degrees times k, where k is an integer...