Inverse Cosine Calculator
Find the inverse cosine angle in degrees or radians.
Table of Contents
How to Use
- Enter the cosine value between -1 and 1
- Choose your preferred output unit (degrees or radians)
- Set decimal precision if needed
- Calculate to get the principal arccos angle and its complement
Principal value of arccos
arccos(x) returns the angle θ in the range [0, π] whose cosine is x. This keeps the inverse single-valued.
The supplementary angle π - θ has the same cosine, which is why both results appear on the unit circle's upper half.
Common uses of inverse cosine
- Finding angles from dot products in vector geometry
- Recovering triangle angles from side lengths via the law of cosines
- Converting between orientation formats in robotics and navigation
Frequently Asked Questions
- Why is the output restricted to [0, π]?
- Cosine is not one-to-one, so the inverse is defined on a principal range to stay single-valued. Other angles with the same cosine can differ by integer multiples of 2π.
- What is the difference between θ and π - θ?
- Both angles share the same cosine. θ is the principal value, while π - θ is the supplementary angle on the unit circle's upper arc.
- Can I enter values outside [-1, 1]?
- No. Cosine outputs stay within [-1, 1], so arccos is only defined on that domain for real angles.