lightbulb Key Concepts

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1. Principal Solutions

The solutions of a trigonometric equation for which 0 ≤ x < 2π are called principal solutions.

2. General Solutions

• sin x = sin α: x = nπ + (-1)ⁿ α, n ∈ Z
• cos x = cos α: x = 2nπ ± α, n ∈ Z
• tan x = tan α: x = nπ + α, n ∈ Z

3. Quadratic Form

Equations like a sin² x + b sin x + c = 0 can be solved by substituting u = sin x and using quadratic methods.