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This question already has an answer here:

Just as a simple example, say I wanted to solve Sin[x] == a for x with the constraints -1<=a<=1 and 0 < x < Pi. Is there any way to do this?

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marked as duplicate by Dr. belisarius, Artes, Sjoerd C. de Vries, István Zachar, Pinguin Dirk Oct 1 '13 at 20:27

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Solve[Sin[x] == a && -1 <= a <= 1 && 0 < x < Pi, x] $\endgroup$ – Artes Oct 1 '13 at 18:56
  • $\begingroup$ You should browse another questions on equation-solving. Solve here is just an adequate approach, but in more general cases one would rather use Reduce or Solve[..., MaxExtraConditions-> All]. Take a look at What is the difference between Reduce and Solve? or How do I work with Root objects? $\endgroup$ – Artes Oct 1 '13 at 19:07