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Home » First, compute the GCD of 48 and 72. The prime factorizations are: - SUpost

First, compute the GCD of 48 and 72. The prime factorizations are: - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 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^\ci...
Let $ \theta = 2z + 60^\circ $, so:
2z + 60^\circ = 30^\circ + 360^\circ k \Rightarrow 2z = -30^\circ + 36...
2z + 60^\circ = 150^\circ + 360^\circ k \Rightarrow 2z = 90^\circ + 36...
Now find all $ z \in [0^\circ, 360^\circ] $:
For $ z = -15^\circ + 180^\circ k $:
$ k = 1 $: $ 165^\circ $
$ k = 2 $: $ 345^\circ $

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