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Home » The Ultimate Martian Manhunter Guide: Legend or Overrated Classic? - Upplift

The Ultimate Martian Manhunter Guide: Legend or Overrated Classic? - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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Solution: Convert to Cartesian coordinates using $\rho = \sqrt{x^2 + y...
\rho^2 = 2\rho \sin\phi \cos\theta \implies x^2 + y^2 + z^2 = 2x.
Rearranging:
x^2 - 2x + y^2 + z^2 = 0 \implies (x^2 - 2x + 1) + y^2 + z^2 = 1 \impl...
This is a sphere centered at $(1, 0, 0)$ with radius 1.
\boxed{\text{A sphere of radius 1 centered at } (1, 0, 0)}
Question: Find the maximum value of $\left(\sin x + \csc x\right)^2 +...
Solution: Expand the expression:
Simplify using $\sin^2 x + \cos^2 x = 1$ and $\csc^2 x = 1 + \cot^2 x$...
+ 2 + 2 + \cot^2 x + \tan^2 x = 5 + \cot^2 x + \tan^2 x.

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