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📅 May 4, 2026 👤 scraface

May 04, 2026

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5Question: Among all solutions to $ \cos(3\theta) = \frac{\sqrt{3}}{2}...
We begin by solving the equation:
\cos(3\theta) = \frac{\sqrt{3}}{2}
The general solution for $ \cos \phi = \frac{\sqrt{3}}{2} $ is:
\phi = 30^\circ + 360^\circ k \quad \text{or} \quad \phi = 330^\circ +...
Since $ \phi = 3\theta $, we substitute:
3\theta = 30^\circ + 360^\circ k \quad \Rightarrow \quad \theta = 10^\...
3\theta = 330^\circ + 360^\circ k \quad \Rightarrow \quad \theta = 110...
We now find all $ \theta \in [0^\circ, 360^\circ] $ by plugging intege...
For $ \theta = 10^\circ + 120^\circ k $:

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