How to Calculate Arccos
What is Arccos?
Arccos (inverse cosine, cos⁻¹) returns the angle whose cosine equals the input value. The output is in the range [0°, 180°] or [0, π] radians.
Formula
θ = arccos(x) where cos(θ) = x
- x
- input value (cosine) — must be in range [−1, 1]
- θ
- angle result (degrees or radians)
Step-by-Step Guide
- 1arccos(x) returns θ where cos(θ) = x
- 2Domain: x ∈ [−1, 1]
- 3Range: [0°, 180°] or [0, π] radians
- 4arccos(0.5) = 60°, arccos(−1) = 180°
Worked Examples
Input
arccos(0.5)
Result
60° or π/3 radians
Input
arccos(0)
Result
90° or π/2 radians
Input
arccos(−0.5)
Result
120° or 2π/3 radians
Frequently Asked Questions
What is the domain and range of arccos?
Domain: [−1, 1]. Range: [0°, 180°] or [0, π] radians.
Why is arccos(1) = 0 and arccos(−1) = 180°?
cos(0°) = 1, so the angle whose cosine is 1 is 0°. Similarly, cos(180°) = −1.
Is arccos the same as 1/cos?
No! arccos is the inverse function (angle from cosine). 1/cos is the reciprocal (secant).
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