00:01
For this problem, we want to find the exact value of cosine 13 pi over 12 if cosine pi over 6 equals square root 3 over 2.
00:10
Let's start with cosine 13 pi over 12.
00:18
We know that the reference angle of 13 pi over 12 is pi over 12.
00:24
So that means that cosine 13 pi over 12 is going to equal cosine pi over 12.
00:36
But you see cosine 13 pi over 12 is on the third quadrant and we know that cosine 13 pi over 12 on the third quadrant is going to be a negative answer.
00:52
However, cosine pi over 12 is on the first quadrant, which gives us a positive answer.
00:59
So in order for these two to be equal, i need to put a minus in front of the cosine pi over 12.
01:05
That way they're both are going to be negative.
01:09
Then i know that negative cosine pi over 12 is the same thing as negative cosine pi over 6 divided by 2.
01:22
So pi over 6 divided by 2 is pi over 12.
01:25
So that's why these two are equal.
01:28
So now i'm going to use a half angle formula, which is cosine half of a, is equal to plus or minus the square root of 1 plus cosine, a divided by 2.
01:50
So i'm going to find what this is right here.
01:55
So i'm not going to worry about this negative right now.
01:58
I'm just going to worry about cosine pi over 6 over 2.
02:06
Okay? i'm not going to worry about the negative right now.
02:08
Now here, the a is going to be my pi over six.
02:13
So if i soft it to pi over six for the a in the formula, i'm going to get 1 plus cosine pi over 6 over 2...