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4! = 24 - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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🔥 Popular Posts

2\cos\theta = \sqrt{3} \Rightarrow \cos\theta = \frac{\sqrt{3}}{2}
\Rightarrow \theta = 30^\circ \text{ or } 330^\circ
Smallest positive is $30^\circ$. But not matching. Re-express the iden...
\cos(\theta + 60^\circ) + \cos(\theta - 60^\circ) = 2\cos\theta\cos 60...
So equation is $\cos\theta = \sqrt{3}$ — impossible. Therefore, the on...
\Rightarrow \cos\theta = 1 \Rightarrow \theta = 0^\circ
Still not positive. Next: suppose the equation is:
\cos(\theta + 60^\circ) + \cos(\theta - 60^\circ) = \frac{1}{2}
\Rightarrow \cos\theta = \frac{1}{2}
\Rightarrow \theta = 60^\circ, 300^\circ, \dots

📝 Recent Posts

We test integer values of \( x \) from \( -5 \) to \( 5 \), since \( x...
For each \( x \), check if \( 225 - 9x^2 \) is divisible by 25 and the...
\( x = 0 \): \( 9(0) + 25y^2 = 225 \Rightarrow y^2 = 9 \Rightarrow y =...
\( x = \pm 1 \): \( 9(1) = 9 \Rightarrow 25y^2 = 216 \Rightarrow y^2 =...
\( x = \pm 2 \): \( 9(4) = 36 \Rightarrow 25y^2 = 189 \Rightarrow y^2...
\( x = \pm 3 \): \( 9(9) = 81 \Rightarrow 25y^2 = 144 \Rightarrow y^2...
\( x = \pm 4 \): \( 9(16) = 144 \Rightarrow 25y^2 = 81 \Rightarrow y^2...
\( x = \pm 5 \): \( 9(25) = 225 \Rightarrow 25y^2 = 0 \Rightarrow y =...
Total lattice points: \( (0, \pm3), (\pm5, 0) \) → 4 points.
Thus, the number of lattice points is \( \boxed{4} \).

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