Inverse Tangent (Arctan) Calculator Formula

Understand the math behind the inverse tangent (arctan) calculator. Each variable explained with a worked example.

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Formulas Used

Angle Rad

angle_rad = atan(val)

Angle Deg

angle_deg = atan(val) * 180 / pi

Variables

VariableDescriptionDefault
valValue1

How It Works

Inverse Tangent (Arctan)

Definition

arctan(x) = the angle whose tangent is x

Domain and Range

  • Domain: all real numbers
  • Range: -90° to 90° (-pi/2 to pi/2 radians)

    • Unlike arcsin and arccos, arctan accepts any real number as input.

    Worked Example

    Find arctan(1).

    val = 1
    1. 01arctan(1) = pi/4 radians
    2. 02= 45 degrees
    3. 03Verification: tan(45°) = 1

    Frequently Asked Questions

    What is arctan?

    Arctan (inverse tangent) returns the angle whose tangent equals the given value. Unlike arcsin/arccos, it accepts any real number.

    What is arctan used for?

    Arctan is used to find angles from slope ratios, in navigation, physics (angle of elevation/depression), and computer graphics.

    What is the difference between arctan and atan2?

    atan2(y, x) takes two arguments and returns the angle in the correct quadrant (-180° to 180°). arctan only returns angles from -90° to 90°.

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