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Home » Third term: $ A + 2d $, first: $ A $, so ratio: - Feedz API

Third term: $ A + 2d $, first: $ A $, so ratio: - Feedz API

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 \sin(2z + 60^\circ) = 1 \Rightarrow \sin(2z + 60^\circ) = \frac{1}{2}

📌 The general solution for $ \sin \theta = \frac{1}{2} $ is:

📌 \theta = 30^\circ + 360^\circ k \quad \text{or} \quad \theta = 150^\circ + 360^\circ k

📌 Let $ \theta = 2z + 60^\circ $, so:

📌 2z + 60^\circ = 30^\circ + 360^\circ k \Rightarrow 2z = -30^\circ + 360^\circ k \Rightarrow z = -15^\circ + 180^\circ k

📌 2z + 60^\circ = 150^\circ + 360^\circ k \Rightarrow 2z = 90^\circ + 360^\circ k \Rightarrow z = 45^\circ + 180^\circ k

📌 Now find all $ z \in [0^\circ, 360^\circ] $:

📌 For $ z = -15^\circ + 180^\circ k $:

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