00:01
Okay, so they give us that sign of theta equals 7 over 11, and it's in the second quadrant.
00:13
So sign is your opposite over your hypotenuse.
00:18
And so if i do pythagorean theorem, a squared plus b squared equals c squared.
00:24
I'm going to get a squared plus 49 equals 121.
00:29
When i subtract 49.
00:32
Oops, let's make this a lot here.
00:37
I'm going to get a squared equals 72.
00:41
And when i square root that, square root is 72.
00:45
In radical form, i can break down to square to 36 and 2.
00:50
Square to 36 is 6.
00:53
I'm going to leave it square root of 2.
00:54
And since i'm going to the left, i'm going to make this negative 6 times square to 2.
01:01
Then it wants three things.
01:03
So it wants sine of 2 theta.
01:08
So the formula for that is to sine theta, cosine theta.
01:14
So we're just going to get those off of our triangle.
01:18
So two times our sign is our opposite over our hypotenuse, our cosine.
01:25
So this is our opposite.
01:26
This is our adjacent.
01:27
This is our hypotenuse from our angle.
01:31
That's theta.
01:33
That's our angle there.
01:34
But cosine is our adjacent over our hypotenuse.
01:41
And when i multiply that out, you're going to get negative 84 squared of 2 over 121.
01:50
And that doesn't reduce.
01:53
The next one is cosine of 2 theta, and there's three formulas.
02:02
So there's cosine squared theta minus sine squared theta, or there's two cosine squared theta minus 1, or there's 1 minus 2 sine square theta.
02:20
And because we were given sine squared originally, i'm going to use this one right here.
02:25
That way, in case we messed up our triangle, we know that it's going to be a good problem to do.
02:32
So 1 minus sine square theta...