# How to solve arcsin(x1/x2 * sin(theta)

$$f = \arcsin\left(\frac {x_1}{x_2} * \sin(\theta)\right)$$

I think this is a simple question, but is there an easy way of solving this equation? Is there a way to solve without having to sin both sides of the equation? Is there some sort of trigonometric identity I can use for this issue?

Thanks!

• What is the unknown? – mvw Feb 26 '15 at 21:17
• You have three symbolic quantities (with unstated meaning) on the right. Could you please clarify what you mean by "solve"? – Andrew D. Hwang Feb 26 '15 at 21:17
• Sorry, to clarify, I meant simplify. So if I had $arcsin(sin(\theta))$ it would equal $\theta$, but how would I go about simplifying the expression above symbolically? – PenguinCy Feb 26 '15 at 21:20
• What variable do you need to get? – 3d0 Feb 26 '15 at 21:43

$$y=\arcsin (x)$$ means $$\sin y=x$$ so ....
$$\sin f=\dfrac{x_1}{x_2} \sin \theta$$
$$x_2 \sin f=x_1 \sin \theta$$