arcsin(√2/2) = 45° (π/4)
Inverse Trigonometric Table
This inverse trigonometric table provides principal values for arcsin(x), arccos(x), and arctan(x), shown in both degrees and radians. Note that arcsin(x) and arccos(x) are real-valued only for x ∈ [−1, 1], while arctan(x) is defined for all real numbers.
In the tables below, a dash (—) indicates that the input is not part of the standard “common exact values” set for that function in this quick reference (not that the function is undefined).
Inverse Trigonometric Calculator
Enter a value to find its arcsine, arccosine, and arctangent.
arcsin30
arccos60
arctan26.565051
Inverse Trigonometric Values
| Input (x) | arcsin(x) | arccos(x) | arctan(x) |
|---|---|---|---|
| −√3 | — | — | −60° (−π/3) |
| −1 | −90° (−π/2) | 180° (π) | −45° (−π/4) |
| −√3/2 | −60° (−π/3) | 150° (5π/6) | — |
| −√2/2 | −45° (−π/4) | 135° (3π/4) | — |
| −1/2 | −30° (−π/6) | 120° (2π/3) | — |
| 0 | 0° (0) | 90° (π/2) | 0° (0) |
| 1/2 | 30° (π/6) | 60° (π/3) | — |
| √2/2 | 45° (π/4) | 45° (π/4) | — |
| √3/2 | 60° (π/3) | 30° (π/6) | — |
| 1 | 90° (π/2) | 0° (0) | 45° (π/4) |
| √3 | — | — | 60° (π/3) |
Understanding Inverse Trigonometric Values
Trigonometric functions are periodic, so the same ratio can correspond to multiple angles. Inverse trigonometric functions resolve this by returning angles only within a principal range (also called the principal value).
- arcsin(x): Domain [−1, 1], Range [−90°, 90°] (i.e., [−π/2, π/2])
- arccos(x): Domain [−1, 1], Range [0°, 180°] (i.e., [0, π])
- arctan(x): Domain (−∞, ∞), Range (−90°, 90°) (i.e., (−π/2, π/2))
Further reading
If you want a deeper conceptual explanation (graphs, identities, and worked examples), these are good references:
Quick Examples
arccos(−1/2) = 120° (2π/3)
arctan(√3) = 60° (π/3)