How should I go as to solving an equation, given sin(x)?

So, I'm working out an equation. I'm used to being given sine equations such as sin(10) = x/blabla, but for this one, I am given:

sin(x) = 11/33

I've attempted working it out, like so:

sin(x) = 11/33
sin(33x) = 11/33 * 33
sin(33x) = 11
After this, I'm not sure what the next step would be, so I simply divided, giving me x = 0.33.
Would that mean that I am left with sin(0.33), resulting in 0.00575955? I feel like I have done this equation incorrectly.

Question

How should I go as to solving an equation, given sin(x)?

So, I'm working out an equation. I'm used to being given sine equations such as sin(10) = x/blabla, but for this one, I am given:

sin(x) = 11/33

I've attempted working it out, like so:

sin(x) = 11/33
sin(33x) = 11/33 * 33
sin(33x) = 11
After this, I'm not sure what the next step would be, so I simply divided, giving me x = 0.33.
Would that mean that I am left with sin(0.33), resulting in 0.00575955? I feel like I have done this equation incorrectly.

anonymous · Answer

to solve for x when x is in the argument of a trigonometric function you must take the inverse of both sides.

anonymous · Answer

$$\sin^{-1} (x) = x$$ This is what you should use to solve for x.