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Home » Let \( x = \sin \theta \), so: - Groen Casting

Let \( x = \sin \theta \), so: - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📝 Recent Posts

÷ 18 = 52.5 → not
This pattern suggests θ = 45(2k+1), so θ = 90k + 45 → always ≡45 mod 9...
But is 90k + 45 divisible by 18?
mod 18 = 9 → so 90k mod 18 = 0, 45 mod 18 = 9 → so θ mod 18 = 9 → not...
Ah! Critical error: step size 18 → angle must be divisible by 18 to be...
But 45 is not divisible by 18. So can the robotic arm reach 45°? Only...
In fact, only angles divisible by gcd(18,45) = 9° are reachable? No —...
The general reachable angles are all integer multiples of 9°, but only...
18n = 9×2n → so all multiples of 18° are reachable, but not all multip...
Specifically, 18n = 45k → 2n = 5k → n = 5m, k = 2m → 18×5m = 90m° → so...

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