Inverse Trigonometric Functions — Chapter Summary

Trigonometric functions like sin

Trigonometric functions like sin, cos, tan are not one-one and onto over their entire domains. For example, sin(π/6) = sin(5π/6) = 1/2, meaning multip

The function sin⁻¹

The function sin⁻¹: [-1, 1] → [-π/2, π/2] is the principal value branch of the inverse sine function. If y = sin⁻¹(x), then sin(y) = x and -π/2 ≤ y ≤

The function cos⁻¹

The function cos⁻¹: [-1, 1] → [0, π] is the principal value branch of the inverse cosine function. If y = cos⁻¹(x), then cos(y) = x and 0 ≤ y ≤ π. For

The function tan⁻¹

The function tan⁻¹: ℝ → (-π/2, π/2) is the principal value branch of the inverse tangent function. If y = tan⁻¹(x), then tan(y) = x and -π/2 < y < π/2

cot⁻¹

cot⁻¹: ℝ → (0, π) with the property that cot⁻¹(x) + tan⁻¹(x) = π/2. sec⁻¹: ℝ - (-1, 1) → [0, π] - {π/2} with sec⁻¹(x) = cos⁻¹(1/x). cosec⁻¹: ℝ - (-1,