lightbulb Key Concepts

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1. Introduction

Inverse trigonometric functions (like sin⁻¹ x or arcsin x) are the inverse functions of the trigonometric functions with restricted domains.

2. Principal Value Branch

• sin⁻¹ x: [-π/2, π/2]
• cos⁻¹ x: [0, π]
• tan⁻¹ x: (-π/2, π/2)

3. Properties

• sin(sin⁻¹ x) = x
• sin⁻¹(-x) = -sin⁻¹ x
• cos⁻¹(-x) = π - cos⁻¹ x
• tan⁻¹ x + cot⁻¹ x = π/2