Free · Trigonometry calculators 📐

Six Principal Inverse Trigonometric Functions

Select arcsine, arccosine, arctangent, arccotangent, arcsecant or arccosecant and convert its principal angle among supported units.

Formula & worked example
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Calculator inputs

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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Arctangent of one is π/4 radians, or 45°.

y = selected inverse trigonometric function of x

Worked example

Enter these known values and leave the other values blank.

Inverse trigonometric function: arctan
x: 1

arctan(x): 0.7854 rad

Assumptions and limitations

Arcsine and arccosine require x from −1 through 1. Arcsecant and arccosecant require |x| ≥ 1. Arctangent and arccotangent accept real x.
Principal ranges are arcsine [−π/2,π/2], arccosine [0,π], arctangent (−π/2,π/2), and corresponding reciprocal-function ranges.
Arccotangent here uses atan(1/x) for nonzero x and π/2 at zero. Negative inputs therefore give negative acute angles, rather than the alternative 0-to-π convention used in some texts.
Only the selected function is shown; undefined values of other hidden functions are not results.
Arithmetic uses 64 significant decimal digits, with separate rounding for displayed values.

Common questions

Why can two arccotangent references give different angles?

They may choose different principal ranges. This tool uses a negative angle for negative nonzero x, and π/2 at zero.

References

Calculation definition and unit reference

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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