Free · Mathematical relations and geometry
Principal Arctangent with Angle Units
Convert a tangent ratio to its principal arctangent angle, with degrees, radians and other angle units.
- Formula & worked example
- Private in your browser
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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
The principal arctangent of 1 is 45°, and the principal arctangent of −1 is −45°.
y=arctan x; x=tan y
Worked example
Enter these known values and leave the other values blank.
- x
- 1
- y
- 45 deg
Assumptions and limitations
- Principal arctangent lies strictly between −90 and 90 degrees, excluding endpoints.
- Changing the angle unit preserves the same angle. It does not change the dimensionless tangent input.
- Entering a valid principal angle solves for its tangent. Other tangent solutions differ by integer multiples of 180 degrees.
Common questions
How can I solve for a missing quantity?
Leave the unknown control empty and enter the quantities needed by the selected relation. Read the assumptions for any branch or domain restrictions.
How should I interpret the worked example?
It is an exact mathematical model with independently checked numbers. Display rounding does not change the values used for subsequent calculations.
References
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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