00:01
Alright, question 40.
00:04
I'm going to start with a drawing.
00:09
So here's my, so my arc length is 5.
00:25
And my cord is 4.
00:34
Make this my a.
00:39
This is also my a, because it's my radius.
00:45
All right, so a is my radius.
00:48
And my cord ab equals 4.
01:01
So i have a times theta, therefore 5 equals a times theta a equals 5 divided by theta.
01:37
So i'm going to use my law of cosines which says c squared, which is my 4 squared, my cord length, equals a squared plus b squared, but a squared and b squared are the same.
02:01
So i'm going to have a squared plus a squared minus 2ab, which is 2a squared cosine theta.
02:17
So now i'm going to plug in my 4 for my c.
02:26
Equals and i'm going to factor out.
02:30
I'm going to simplify.
02:32
I have 2a squared minus 2a squared cosine theta.
02:42
16 equals 2a squared 1 minus cosine theta.
02:55
8 equals so i just divided by 2.
03:01
So now i have a squared, 1 minus cosine theta.
03:11
I'm going to replace a with what my a is, 5 divided by theta.
03:18
8 equals 5 over theta squared, 1 minus cosine theta.
03:32
8 equals 25 over theta squared.
03:39
1 minus cosine theta...