Inverse Trigonometric Functions Calculator

Inverse trigonometric functions are the inverses of the standard trig functions. For example, arcsin(x) gives you the angle whose sine equals x. They are used to find an angle when you know the ratio of sides in a right triangle. The six inverse trig functions are arcsin, arccos, arctan, arccot, arcsec, and arccsc.

arcsin(0.5) = 30° (or π/6 radians). This is because sin(30°) = 0.5. Note that the principal value is always returned — in this case 30°, not the equivalent 150°, because arcsin is restricted to the range [−90°, 90°].

For arcsin and arccos, x must be between −1 and 1 (inclusive). For arctan and arccot, x can be any real number (arccot excludes 0 in some conventions). For arcsec and arccsc, |x| must be greater than or equal to 1 (i.e., x ≤ −1 or x ≥ 1). Entering a value outside the domain will produce an error.

arcsin returns the angle whose sine equals x (range: −90° to 90°). arccos returns the angle whose cosine equals x (range: 0° to 180°). arctan returns the angle whose tangent equals x (range: −90° to 90°, exclusive). Each has a different domain and restricted range to ensure a unique (principal) output value.

Because inverse trig functions return only the principal value — one unique angle within a defined restricted range. Since sin(30°) = sin(150°) = 0.5, we need a convention, so arcsin is restricted to [−90°, 90°]. If you need all angles that satisfy the equation, you would use the general solution: θ = 30° + 360°n or θ = 150° + 360°n for integer n.

The domain (valid input range) for arccos is −1 ≤ x ≤ 1. The output (range) is between 0° and 180° (or 0 to π radians). Entering any value outside [−1, 1] is undefined for arccos.

Yes. You can choose your preferred output unit — degrees or radians — using the Output Angle Unit option. The table at the bottom always shows results in both units simultaneously for all six inverse trig functions.

Inverse trig functions are widely used in engineering, physics, navigation, and computer graphics. Common applications include calculating the angle of elevation or depression, finding angles in right triangles when side lengths are known, signal processing, and determining angles in 3D rotations and vector analysis.