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Home » Probability of all failures = 0.30³ = 0.027 - ClickBalance

Probability of all failures = 0.30³ = 0.027 - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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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^\ci...
If \( \sin \theta = -1 \), then \( \theta = 270^\circ \)
Check each solution in the original equation:
\( \theta = 30^\circ \): \( \cos 60^\circ = \frac{1}{2},\ \sin 30^\cir...
\( \theta = 150^\circ \): \( \cos 300^\circ = \frac{1}{2},\ \sin 150^\...
\( \theta = 270^\circ \): \( \cos 540^\circ = \cos 180^\circ = -1,\ \s...
All are valid.
\boxed{30^\circ,\ 150^\circ,\ 270^\circ}

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