Free Β· Trigonometry calculators π
Principal Inverse Tangent in Degrees and Radians
They are tangent poles and cannot correspond to a finite real input. Principal arctangent returns an angle strictly between these limits; degree, radian and other selectors represent that same branch.
- 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
Example in initial displayed units: x 1 gives y 45.
y = arctan x; βΟ/2 < y < Ο/2
Worked example
Enter these known values and leave the other values blank.
- x
- 1
- y
- 45 deg
Assumptions and limitations
- This is the principal real inverse tangent, with output strictly between β90Β° and 90Β°. Every finite real input is allowed by the mathematical model. Entering an output angle solves x = tan y only within the principal interval; endpoints are poles rather than finite inputs. Arithmetic and display have finite precision.
- Use compatible units and enough independent values. Clear unknowns before solving backward. Original reference drawings are schematic and do not scale to entered values.
Common questions
Why are 90 degrees and β90 degrees excluded?
They are tangent poles and cannot correspond to a finite real input. Principal arctangent returns an angle strictly between these limits; degree, radian and other selectors represent that same branch.
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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