Solve x = sin(t) for t

Question

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

score 2 · Accepted Answer · answered Feb 19 '12 at 14:27

2

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

answered Feb 19 '12 at 14:27

Julius

1

What have I done wrong then? http://www.wolframalpha.com/input/?i=y%3D13cos%28arcsin%28x%2F16%5E1%2F3%29%29-5cos%282arcsin%28x%2F16%5E1%2F3%29%29-2cos%283arcsin%28x%2F16%5E1%2F3%29%29-cos%284arcsin%28x%2F16%5E1%2F3%29%29 – 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
@Potatoswatter Here is the primary question: http://math.stackexchange.com/questions/110961/solving-parametric-equation-multiple-coefficients-of-trigonomic-functions – Kian Feb 19 '12 at 18:04

1 Answers1