Solving a simple trigonometric equation in a range

I would like to solve a simple trigonometric equation, for example sinθ=12,\sin\theta=\frac{1}{2}, but Solve gives the single solution obtained by using the inverse function ArcSin, while Reduce gives all solution in a form difficult to use.

I would like to have a list of substitutions like the output of Solve, for all solutions contained in a given range, for example [0,2π):[0,2\pi):

{{θ -> π/6}, {θ -> 5π/6}}



1 Answer


You can give explicit ranges as inputs to Solve

Solve[{Sin[t] == 1/2, 0 <= t < 2 π}, t] (* {{t -> π/6}, {t -> (5 π)/6}} *)



How simple! Thank you!
– enzotib
Jan 25 at 16:35