Calculator
Example data table
These are sample rows to illustrate typical outputs.
| Function | Input | Radians (approx) | Degrees (approx) | π multiple |
|---|---|---|---|---|
| asin | 0.5 | 0.523599 | 30 | π/6 |
| acos | 0 | 1.570796 | 90 | π/2 |
| atan | 1 | 0.785398 | 45 | π/4 |
| acot | 1 | 0.785398 | 45 | π/4 |
| atan2 | y=1, x=-1 | 2.356194 | 135 | 3π/4 |
Formula used
Inverse trigonometric functions return a principal value angle that satisfies the original trig relation. Let the output angle be y (in radians).
- y = asin(x) where x ∈ [-1, 1], range [-π/2, π/2].
- y = acos(x) where x ∈ [-1, 1], range [0, π].
- y = atan(x) for any real x, range (-π/2, π/2).
- y = acot(x) defined here with range (0, π).
- y = asec(x) = acos(1/x) where |x| ≥ 1.
- y = acsc(x) = asin(1/x) where |x| ≥ 1.
- y = atan2(y, x) returns an angle based on the point (x, y).
Conversions: degrees = radians × 180/π, and π multiple = radians ÷ π.
How to use this calculator
- Select an inverse function (asin, acos, atan, and others).
- Enter one value or a list separated by commas or spaces.
- For atan2, enter matching y-values and x-values lists.
- Choose degrees, radians, or π-multiple as your preferred output.
- Press Calculate to view results above the form.
- Use Download CSV or Download PDF to export your table.
FAQs
1) Why does asin(0.5) return only 30°?
Inverse functions return a principal value by convention. Although many angles share the same sine, arcsin returns an angle in the range −90° to 90°.
2) What input range works for acos and asin?
Both require x between −1 and 1 inclusive. If you type a slightly out-of-range value due to rounding, enable clamping to correct tiny numeric drift.
3) What is the difference between atan and atan2?
atan uses a single ratio x and returns an angle in (−90°, 90°). atan2 uses (y, x) to determine the correct quadrant, producing angles in (−180°, 180°].
4) Why is arccot defined differently in some books?
Some define arccot with different principal ranges. This calculator uses the common range (0, π) so outputs are positive and map smoothly across quadrants.
5) When can I use arcsec and arccsc?
Use arcsec(x) and arccsc(x) only when |x| ≥ 1. They are computed as acos(1/x) and asin(1/x) and still return principal values.
6) What does the π multiple column mean?
It expresses the radian angle as a multiple of π. When close to a simple fraction, the tool shows a fraction like π/6; otherwise it shows a decimal multiple.
7) Can I enter fractions like 3/4?
Yes. Write inputs as decimals or simple fractions such as 1/2, -3/4, or 5/2. More complex expressions are intentionally blocked for safety.
8) Why is PDF export “simple”?
The PDF is generated directly without extra libraries, so it focuses on clean text output. For rich formatting, export CSV and format it in a spreadsheet tool.