Evaluate arcsin, arccos, arctan, arccsc, arcsec, and arccot at any value. Exact results at standard angles, restricted domain explanations, and an interactive graph with your point highlighted.
Trig functions are periodic — they repeat their values infinitely. That means sin(π/6) = sin(5π/6) = 1/2, so sin is not one-to-one on all of ℝ. An inverse function can only exist when the original function is one-to-one.
The solution: restrict the domain of each trig function to a specific interval where it is one-to-one and covers the full range of outputs. The inverse function's domain is then exactly that restricted interval's output range, and its range is the restricted domain.
The chosen intervals are called principal value ranges — they are the conventional choices used worldwide.
| Function | Domain | Range (radians) | Range (deg) |
|---|---|---|---|
| arcsin | [−1, 1] | [−π/2, π/2] | [−90°, 90°] |
| arccos | [−1, 1] | [0, π] | [0°, 180°] |
| arctan | (−∞, ∞) | (−π/2, π/2) | (−90°, 90°) |
| arccsc | |x| ≥ 1 | [−π/2, 0) ∪ (0, π/2] | [−90°,0°)∪(0°,90°] |
| arcsec | |x| ≥ 1 | [0, π/2) ∪ (π/2, π] | [0°,90°)∪(90°,180°] |
| arccot | (−∞, ∞) | (0, π) | (0°, 180°) |
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