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Home » 30^\circ + 60^\circ + 210^\circ + 240^\circ = 540^\circ - Abu Waleed Tea

30^\circ + 60^\circ + 210^\circ + 240^\circ = 540^\circ - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 x = \frac{-1 \pm \sqrt{1^2 - 4(2)(-1)}}{2(2)} = \frac{-1 \pm \sqrt{1 + 8}}{4} = \frac{-1 \pm 3}{4}

📌 This gives:

📌 x = \frac{2}{4} = \frac{1}{2} \quad \text{or} \quad x = \frac{-4}{4} = -1

📌 So, \( \sin \theta = \frac{1}{2} \) or \( \sin \theta = -1 \).

📌 Solve for \( \theta \in [0^\circ, 360^\circ] \):

📌 If \( \sin \theta = \frac{1}{2} \), then \( \theta = 30^\circ, 150^\circ \)

📌 If \( \sin \theta = -1 \), then \( \theta = 270^\circ \)

📌 Check each solution in the original equation:

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