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.

No! arccos is the inverse function (angle from cosine). 1/cos is the reciprocal (secant).

Mathematics

Value (must be in [−1, 1] for sin/cos)

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.

Symbol	Name	Unit	Description
x	input value (cosine)	—	must be in range [−1, 1]
θ	angle result	degrees or radians	—

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