Inverse Trigonometric Functions — Formula Sheet

A function f is periodic if there exists p > 0 such that f(x + p) = f(x) for all x in the domain.

The inverse sine function is defined as

For -1 ≤ x ≤ 1, sin⁻¹x = y if and only if sin y = x and y ∈ [-π/2, π/2].

The inverse cosine function is defined as

For -1 ≤ x ≤ 1, cos⁻¹x = y if and only if cos y = x and y ∈ [0, π].

The inverse tangent function is defined as

For any real number x, tan⁻¹x = y if and only if tan y = x and y ∈ (-π/2, π/2).

The inverse cosecant function is defined as

For x ∈ ℝ \ (-1, 1), csc⁻¹x = y if and only if csc y = x and y ∈ [-π/2, 0) ∪ (0, π/2].