What is the domain and range of arcsin?

Domain: [−1, 1]. Range: [−90°, 90°] or [−π/2, π/2] radians.

Why does arcsin only return angles up to 90°?

The principal range of arcsin is restricted to avoid ambiguity, since multiple angles can have the same sine value.

arcsin(x) = arccsc(1/x), just like sin and csc are reciprocals.

Mathematics

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

Arcsin (inverse sine, sin⁻¹) returns the angle whose sine equals the input value. The output range is [−90°, 90°] or [−π/2, π/2] radians.

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

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