Inverse Trig Calculator
Turn a sine, cosine, or tangent ratio back into an angle. Get the principal value in degrees and radians, with the right range for arcsin, arccos, and arctan.
Principal angle
From ratio back to angle
Inverse trig functions answer the question “what angle produces this ratio?” They are the tool you reach for when you know two sides of a right triangle and want the angle between them, or when you’re solving a trig equation. Because each ratio matches many angles, every inverse function returns a single principal value from a fixed range.
This calculator shows that principal angle in both degrees and radians and reminds you of the valid input and output ranges, so you know when to reach for a reference angle to reach another quadrant.
Frequently Asked Questions
What does an inverse trig function do?
It runs the trig ratios backwards. Where sine turns an angle into a ratio, arcsine (sin⁻¹) turns a ratio back into an angle. So if you know that the sine of some angle is 0.5, arcsine tells you the angle is 30°. The same idea applies to arccosine and arctangent.
Why is there a restricted range for each function?
Many different angles share the same sine, cosine, or tangent, so an inverse function must pick just one to be well defined. By convention arcsin returns −90° to 90°, arccos returns 0° to 180°, and arctan returns −90° to 90°. These are called the principal values.
Why can't I take arcsin or arccos of a number bigger than 1?
Sine and cosine of a real angle always land between −1 and 1, so no angle has a sine of, say, 1.4. Asking for arcsin(1.4) has no real answer, and the calculator flags it. Arctangent, by contrast, accepts any real number because tangent takes every value.
How do I get an angle in a different quadrant?
The tool returns the principal angle. If your problem lives in another quadrant — common when solving triangles or equations — use the returned value as a reference angle and adjust: for sine, the supplementary angle 180° minus the result shares the same sine; for tangent, adding 180° gives another solution.
Educational tool only. Results are the principal values rounded for display; adjust with reference angles for other quadrants as your problem requires.