00:01
In this problem, we were given the cosine theta equals 24 over 25, and the angle is in between 3 pi over 2 and 2 pi.
00:10
I need to find tangent half the angle.
00:14
Well, we have a formula for tangent half the angle, and that is that tangent half the angle is equal to 1 minus cosine theta, divided by sine theta.
00:28
Now i know cosine theta because it was given, but i need to find sine theta so that i can use this formula.
00:36
So let's find sign theta.
00:38
First, we need to know in which quadrant theta is.
00:42
This right here tells me that theta is in the fourth quadrant, right? because it is in between 3 pi over 2 and 2 pi.
00:51
So let me go ahead and draw my angle in the fourth quadrant.
00:59
Then to find sign, i know that cosine is adjacent over hypotenuse.
01:10
That means that if i draw a right triangle here, adjacent to this angle is going to be 24, and then the hypotenuse is across the 90s, so this is going to be 25.
01:25
Now to find sign data, i need to know this height here, meaning the y.
01:31
So i'm going to apply the pythagorean theorem.
01:35
24 square plus y square equals 25 square.
01:40
If i simplify, i'm going to get 576 plus y square equals 625...