Maybe it's me, but this didn't seem easy!?!? I'm getting an answer of sin a = 1; is this correct?
Here's a summary of what I did:
You have the cosine of a difference identity:
(Eq1)
Use the Law of sines to write sin b in terms of sin a:
(Eq2)
Use the pythagorean identity to write cosine in terms of sine:
(Eq3a)
(Eq3b)
Plug (2), (3a), and (3b) into (1), plus the fact that cos (a-b) = 3/4:
(Eq4)
Solved for sin a and I got sin a = 1.
I'm sure I did something wrong here.
In general , if
The method to find the value of is as follows :
First determine which of the angles is larger by comparing their opposite sides , let's say .
Let be the other point on line such that
Then we have
, by using cosine formula ,
,
Therefore ,