Trying to solve a Trig Equation

Hi There,

I've just joined the forum, and this is my first post. I'm an engineer working on problem with some angle offsets in a device, and would like to be able to solve the following equation. a, b and c are known variables, I am trying to solve for SF, is this possible?

c = Sin^{-1}(a/SF) - Sin^{-1}(b/SF)

Re: Trying to solve a Trig Equation

Re: Trying to solve a Trig Equation

The result from WA looks horrendous, maybe it simplifies ? However, try this instead.

First note that and similarly for

Take the sine of the equation and making use of the expansion for arrive at

(1).

Next, take the cosine of the original equation and having used the expansion for arrive at

(2).

Finally, square (1), make the obvious substitution for the product of the two square roots using (2) and then simplify to arrive at