Inverse Cosine (Arccos) Calculator Formula

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

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Formulas Used

Angle Rad

angle_rad = acos(val)

Angle Deg

angle_deg = acos(val) * 180 / pi

Variables

VariableDescriptionDefault
valValue (-1 to 1)0.5

How It Works

Inverse Cosine (Arccos)

Definition

arccos(x) = the angle whose cosine is x

Domain and Range

  • Domain: -1 ≤ x ≤ 1
  • Range: 0° to 180° (0 to pi radians)

    • Common Values

  • arccos(1) = 0°
  • arccos(0.5) = 60°
  • arccos(0) = 90°
  • arccos(-1) = 180°

    • Worked Example

    Find arccos(0.5).

    val = 0.5
    1. 01arccos(0.5) = pi/3 radians
    2. 02= 60 degrees
    3. 03Verification: cos(60°) = 0.5

    Frequently Asked Questions

    What is arccos?

    Arccos (inverse cosine) returns the angle whose cosine equals the given value. It is the inverse function of cosine.

    Why does arccos range from 0° to 180°?

    This range ensures arccos is a proper function (one output per input). Cosine takes each value in [-1,1] exactly once in the interval [0°, 180°].

    How are arcsin and arccos related?

    arcsin(x) + arccos(x) = 90° for any x in [-1, 1]. They are complementary angles.

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