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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