Trig Equation Solver
Pick a trig function and a value c. The solver returns the two principal solutions in [0, 2π) and the general solution that captures every periodic copy. The reciprocal functions csc, sec and cot are rewritten in terms of sin, cos and tan before solving.
Frequently asked questions
Why are there two principal solutions for sin and cos?
Sine and cosine each take every value in [−1, 1] twice within one period [0, 2π). The two principal solutions correspond to the two angles where the function hits the given value.
What does the general solution mean?
Trig functions repeat — sin and cos every 2π, tan every π. Adding any whole multiple of the period to a solution gives another solution. The general solution captures all of these compactly with a parameter k.
When is there no solution?
When the value is outside the range of the function. For sin and cos that means |c| > 1; csc and sec are equivalent through their reciprocals.