Inverse trig functions answer the question “which angle has this ratio?”: a ramp angle from rise and length, a launch angle from velocities, or the phase of a complex number. Each returns a principal value from a restricted range so the answer is unique.
How to use the Inverse Trigonometric Functions Calculator
- Function
- x
Results update as you type, and everything is calculated in your browser.
How it works
Choose the function and enter x. Arccot, arcsec and arccsc are computed through the reciprocal of x. If x is outside the domain (for example arcsin 2 or arcsec 0.5), the result shows a dash.
Inputs explained
| Field | What to enter |
|---|---|
| Function | Choose one: arcsin, arccos, arctan, arccot … |
| x | A number |
What each result means
- Angle = deg([Angle in radians])
- In radians = [Angle in radians]
- As a multiple of π = [Angle in radians]÷pi
Example values
How the main result changes when x changes and everything else stays at the example values above:
| x | Angle (°) |
|---|---|
| 0.25 | 14.4775 |
| 0.375 | 22.0243 |
| 0.5 | 30 |
| 0.625 | 38.6822 |
| 0.75 | 48.5904 |
| 1 | 90 |
Formula
arcsin x ∈ [−90°, 90°], arccos x ∈ [0°, 180°], arctan x ∈ (−90°, 90°)
arccot x = 90° − arctan x (∈ (0°, 180°)), arcsec x = arccos(1/x), arccsc x = arcsin(1/x)
Worked example
Inputs: Function: arcsin; x: 0.5.
Results: Angle = 30 °; In radians = 0.5235987756 rad; As a multiple of π = 0.16666667 π.
Key terms
- Domain
- The set of inputs a function accepts.
- Range
- The set of values a function returns.
Frequently asked questions
What is the domain of arcsec?
x ≤ −1 or x ≥ 1.
Which range does arccot use?
(0°, 180°), so arccot is continuous; some books use (−90°, 90°].
Why is arcsin(2) not defined?
Sine values lie between −1 and 1.
Are inverse trig functions the same as reciprocals?
No: sin⁻¹x means arcsin x, not 1/sin x.