Cos Inverse Calculator

The inverse cosine function, commonly written as arccos(x) or cos⁻¹(x), is the inverse operation of the standard cosine function. If cos(θ) = x, then arccos(x) = θ. Because the cosine function repeats infinitely, its inverse must be restricted to a specific interval to remain a valid, single-valued function. This calculator processes your input value x using the standard mathematical formula y = arccos(x), ensuring the resulting angle falls strictly within the principal value range.

Imagine you need to find the angle whose cosine is equal to -0.5. First, input -0.5 into the calculator for variable X. The underlying formula evaluates y = arccos(-0.5). Mathematically, we know that the cosine of 120 degrees (or 2π/3 radians) yields -0.5. Therefore, the calculator processes the input and instantly outputs 120° (or approximately 2.0944 radians), providing you with the exact angle needed for your geometric problem.

Always verify that your input value for x stays strictly between -1 and 1, as real-number outputs do not exist outside this domain. Pay close attention to your angle output mode; ensure you have selected degrees or radians depending on whether your engineering or geometry project requires sexagesimal or circular measure.