Inverse Trigonometric Functions

Since trigonometric functions are not one

Since trigonometric functions are not one-to-one over their natural domains, we must restrict their domains to create inverses. For example, sin x is

The principal value branch is

The principal value branch is the specific range we choose for an inverse trigonometric function. For sin⁻¹x, the principal value branch is [-π/2, π/2

Domain

Domain: [-1, 1], Range: [-π/2, π/2]. If y = sin⁻¹x, then sin y = x. The graph is obtained by reflecting y = sin x about the line y = x, restricted to

Domain

Domain: [-1, 1], Range: [0, π]. If y = cos⁻¹x, then cos y = x. The function is decreasing throughout its domain, unlike sin⁻¹x which is increasing.

Domain

Domain: R (all real numbers), Range: (-π/2, π/2). If y = tan⁻¹x, then tan y = x. The function has horizontal asymptotes at y = ±π/2.