Inverse Trig Calculator
Find the angle from a ratio with arcsin, arccos or arctan — answered in degrees, radians and as a multiple of π.
How it works
θ = sin⁻¹(x), cos⁻¹(x) or tan⁻¹(x) · degrees = radians × 180 ÷ π
Inverse trig functions run the ratios backwards: given a value, they return the angle that produces it. Arcsin and arccos only accept inputs from −1 to 1 because sine and cosine never leave that range, while arctan accepts any real number. Each returns a principal value — arcsin and arctan land in [−90°, 90°], arccos in [0°, 180°].
Worked example
arcsin(0.5): which angle has a sine of 0.5? That’s 30°, or π ÷ 6 ≈ 0.523599 radians, so the result shows 30° and 0.1667 π. Feeding 30° back into a sine gives 0.5, closing the loop.
Frequently asked questions
Why does arcsin reject values above 1?
Sine is a ratio of a side to the hypotenuse, and the hypotenuse is always the longest side, so sine never exceeds 1 or drops below −1. No real angle has a sine of 2, so arcsin(2) is undefined.
Which angle do I get back?
The principal value. Infinitely many angles share the same sine, but arcsin returns the one between −90° and 90°; arccos returns 0° to 180°; arctan returns −90° to 90°. Add full turns or reflections to find the rest.
How is this different from cosecant?
Cosecant is 1 ÷ sin — a reciprocal that still takes an angle in and gives a ratio out. The inverse (arcsin) takes a ratio in and gives an angle out. They are not the same operation despite similar notation.
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This calculator is for educational purposes. Double-check important results before acting on them.