00:01
First of all, i would figure out where theta is in quadrant 3.
00:07
So i'm just going to draw it.
00:08
It's not going to be the scale because if cotangent of theta is equal to 14, then tangent of theta is equal to the reciprocal 1 over 14.
00:19
That's definitely not to scale because tangent is opposite over adjacent.
00:25
So the way i've drawn it, the opposite side would be 1 and the adjacent side would be 14.
00:32
Well, they'd both be negative as well.
00:33
So now i would do the pythagorean theorem to see that 1 squared plus 14 squared is equal to the, i like to call it the r value squared.
00:44
Right here is r.
00:45
And when you do, well, 1 squared is 1 and 14 squared is 196.
00:51
So that's 197 when you add it together.
00:54
So r would be equal to the square root of 197.
00:57
So now you can figure out what sine of 2 theta is.
01:03
And all i'm doing is the double angle formula 2 sine of theta, cosine of theta.
01:08
I guess i'm jumping ahead because i should also point out that sine of theta, let's do this in black, is opposite over hypotenuse.
01:17
So it's negative 1 over root 197.
01:21
And while i'm at it, cosine is adjacent over hypotenuse.
01:23
So it's negative 14 over root 197.
01:26
And so as we're looking at this, 2 times negative 1 over root 197 times negative 14 over root 197.
01:39
And a negative times negative is positive...