Inverse Trigonometric Functions — Chapter Summary

A function f is periodic if

A function f is periodic if there exists p > 0 such that f(x + p) = f(x) for all x in the domain. Sine, cosine, cosecant, and secant have period 2π, w

The inverse sine function is defined

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]. Domain: [-1, 1], Range: [-π/2, π/2].

The inverse cosine function is defined

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]. Domain: [-1, 1], Range: [0, π]. Key pro

The inverse tangent function is defined

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). Domain: ℝ (all real number

The inverse cosecant function is defined

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]. Domain: (-∞, -1] ∪