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📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📝 Recent Posts

f(\theta) = (\sin^4 \theta + \cos^4 \theta) - 4\sin^2 \theta \cos^2 \t...
Recall that:
\sin^4 \theta + \cos^4 \theta = (\sin^2 \theta + \cos^2 \theta)^2 - 2\...
Substitute into $ f(\theta) $:
f(\theta) = (1 - 2\sin^2 \theta \cos^2 \theta) - 4\sin^2 \theta \cos^2...
Now use the identity $ \sin(2\theta) = 2\sin\theta \cos\theta $, so:
\sin^2(2\theta) = 4\sin^2\theta \cos^2\theta \Rightarrow \sin^2\theta...
f(\theta) = 1 - 6 \cdot \frac{1}{4} \sin^2(2\theta) = 1 - \frac{3}{2}...
The maximum value of $ \sin^2(2\theta) $ is 1, so the minimum value of...
- \frac{3}{2}(1) = -\frac{1}{2}.

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