00:01
So here we're given that sine of theta is equal to one half, where theta is in the first quadrant.
00:05
What we can start off by doing is finding what cosine of theta is equal to, because all of our double angle and half angle formulas contain cosine of theta.
00:14
So if we draw out the diagram here in quadrant 1, we have theta here, with sine of theta being 1 half, that means that the y is 1 and the radius is 2.
00:26
So to find out what x is equal to, we do the square root.
00:30
Of 2 squared minus 1 squared, which is just the pythagorean theorem, to get root 3.
00:36
Therefore, cosine of theta is equal to x divided by r, which is root 3 divided by 2.
00:45
Now let's start off by finding sign of 2 theta.
00:49
This is equal to 2 times sine of theta, which is 1 1⁄2, times cosine of theta, which is root 3 over 2.
00:56
2 times 1⁄2, so those cancel out, leaving us with root 3.
01:01
Over 2.
01:04
Now for our cosine of 2 theta, we know this is equal to 1 minus 2 sine squared theta...
