If $\sin \theta =37$ then find value of $\theta$ This problem I encountered in my maths book.I know how to find theta which are very basic (30 and 60 and 45).please help me.
 A: Sine takes on values between $-1$ and $1$ (at least for real valued inputs).
So, $\sin \theta = 37$ has no real solution.
A: Hint:
If $\sin\theta = n$, then $\theta = \arcsin n$. However you should notice $\arcsin : [-1,1] \to [-90^\circ, 90^\circ]$, meaning $37$ is not within the domain of $\arcsin$.
A: If you're familiar with things like half- and double-angle formulas, then you can find more general identities that'll relate, for instance, $\sin \theta, \cos \theta$ with $\sin (\theta / n)$ for appropriate numbers, as well as expressions of $\sin n \theta$ in terms of $\sin \theta, \cos \theta$. These could tell you $\sin$ for $37^{\circ}$, but they'll be tedious.
Also, a piece of advice with how you posed your question. If I read you correctly, you're asking "What is the exact value of $\sin \theta$ when $\theta = 37^{\circ}$?" But what you wrote ("If $ \sin \theta = 37$ then find value of $\theta$") was construed by many as asking, "For what angle $\theta$ is $\sin \theta = 37$?", i.e. trying to solve the equation $\sin (\theta) = 37$. This equation, as many pointed out, does not have a real solution, so we must resort to the complex numbers to solve it. You'd do well to (1) take care to phrase your question carefully and clearly so you don't just get unhelpful answers to questions you didn't mean to ask, and (2) get basically familiar with Mathjax, which is not only aesthetically pleasing, but will help you write your question more clearly. A major part of math is learning how to communicate it, and good communication skills will make benefitting from this site a lot easier, as well as help you with your math studies in general.
