Arccosine Calculator

The arccos function, also known as the inverse cosine function, is a mathematical operation that takes a value between -1 and 1 and returns the angle in radians or degrees whose cosine is equal to that value, allowing us to find the original angle given its cosine. It is the inverse of the cosine function and is denoted as arccos(x) or cos^(-1)(x).
arccos⁡(1)=  0\arccos({1})=\;00
Photo of calculator author Wes NolteCreated by Wes Nolte.Last updated Apr 25, 2024.

The Arccosine Calculator Formula

y=arccos⁡(x)=cos⁡−1(x)y = \arccos(x) = \cos^{-1}(x)

Definition of the Arccos Function

The domain of the arccos function is -1 ≤ x ≤ 1, as the cosine function produces values within that range. The range of the arccos function is 0 ≤ arccos(x) ≤ π (or 0° ≤ arccos(x) ≤ 180°), representing the possible angles whose cosine corresponds to the given value.To find the angle, we input a value into the arccos function, and it returns the angle in radians or degrees. For example, if we have the value x = 0.5, we can compute arccos(0.5) to find the angle whose cosine is 0.5. The result would be π/3 (or 60°), indicating that the angle with a cosine of 0.5 is 60 degrees.It's important to note that the arccos function has a restricted domain, and for values outside of -1 ≤ x ≤ 1, it is undefined. Additionally, the arccos function produces a single output for each valid input, but multiple angles may have the same cosine value due to the periodic nature of the cosine function.The arccos function is widely used in mathematics, physics, engineering, and other fields. It helps solve equations involving cosine, find angles in geometric problems, analyze trigonometric functions, and perform inverse trigonometric calculations.