# Solve x = sin(t) for t

How can I solve: $(\frac{x}{16})^{\frac{1}{3}} = \sin(t)$ for t?

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## 1 Answer

$$t=\arcsin\big(\frac{x}{16}\big)^{\frac{1}{3}}$$

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What have I done wrong then? wolframalpha.com/input/… –  Kian Feb 19 '12 at 14:40
@KianMayne You left out parentheses — exponentiation has higher precedence than division. Does this look better? –  Potatoswatter Feb 19 '12 at 15:07
I got it, where I had previously got $$({\frac{x}{16}})^{\frac{1}{3}}$$ it should have been $$\frac{x^{\frac{1}{3}}}{16^\frac{1}{3}}$$ –  Kian Feb 19 '12 at 15:26
@Potatoswatter I noticed that, but as I mentioned ^ there it was a problem with my original calculation –  Kian Feb 19 '12 at 15:28
@KianMayne Hard to tell what's wrong without any context. The two expressions in your comment are the same, exponentiation distributes over multiplication. The mistake was $\frac{x}{16^{1/3}}$. Is there still a problem? –  Potatoswatter Feb 19 '12 at 16:50