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

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!

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  • $\begingroup$ What is the unknown? $\endgroup$ – mvw Feb 26 '15 at 21:17
  • $\begingroup$ You have three symbolic quantities (with unstated meaning) on the right. Could you please clarify what you mean by "solve"? $\endgroup$ – Andrew D. Hwang Feb 26 '15 at 21:17
  • $\begingroup$ 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? $\endgroup$ – PenguinCy Feb 26 '15 at 21:20
  • $\begingroup$ What variable do you need to get? $\endgroup$ – 3d0 Feb 26 '15 at 21:43
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Hint:

$$y=\arcsin (x) $$ means $$\sin y=x$$ so ....

$$ \sin f=\dfrac{x_1}{x_2} \sin \theta $$

and:

$$ x_2 \sin f=x_1 \sin \theta $$

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