Arccos Calculator

arccos(0.5) = 60 degrees (or pi/3 radians). This means the angle whose cosine equals 0.5 is 60 degrees. You can verify: cos(60) = 0.5.

Arccos only accepts values from -1 to 1 (inclusive), because cosine never produces a value outside this range. arccos(-1) = 180 degrees and arccos(1) = 0 degrees are the boundary values. Any input outside [-1, 1] has no real solution.

Cosine produces the same value for multiple angles (e.g., cos(60) = cos(300) = 0.5). To make arccos a proper function with one output per input, it is restricted to [0, 180] degrees. If you need an angle outside this range, use the relationship: the other solution is 360 minus the arccos result.

The angle between vectors A and B is theta = arccos((A dot B) / (|A| x |B|)). Calculate the dot product, divide by the product of magnitudes, then take arccos. For example, vectors (1,0) and (1,1): dot product = 1, magnitudes = 1 and 1.414, so theta = arccos(1/1.414) = arccos(0.7071) = 45 degrees.

They are the same function. arccos, cos^(-1), and acos all refer to inverse cosine. The notation cos^(-1)(x) means "the angle whose cosine is x", not 1/cos(x). The reciprocal of cosine is secant, written sec(x) = 1/cos(x), which is a different operation entirely.

Absolutely. Use the "Embed" option above to tailor the dimensions, color scheme, and styling to match your site. Copy the generated iframe snippet and drop it into your HTML, WordPress editor, or any CMS. There is no cost and no account required. See calculory.com/services/embed-calculators for a step-by-step walkthrough.