Solve trigonometric equations

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Useful for: IB Math AA SL & HL AP® Precalculus

Learn it Isolate the trig function first (like solving for x), then find all angles in the interval using the reference angle and CAST. Quadratic-type equations: factor first, e.g. 2sin²x − sin x − 1 = 0 → (2sin x + 1)(sin x − 1) = 0.

Example: Solve 2cos x + 1 = 0 for 0° ≤ x ≤ 360°.

cos x = −1/2. Reference angle 60°.
Cosine is negative in Q2 and Q3: x = 120° or 240°.

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