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Emil Jeřábek
Emil Jeřábek
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For which $p>p^*$ does the inequality $\rm{cos}^2$\cos^2(−π/4+π/p)>1/2+π/p^2$​ hold?

I have the inequality $\rm{cos}^2(−\frac{\pi}{4}+\frac{\pi}{p})>\frac{1}{2}+\frac{π}{p^2}$$\cos^2(−\frac{\pi}{4}+\frac{\pi}{p})>\frac{1}{2}+\frac{π}{p^2}$​​ and have found that it holds for $p>p^*$, where $p^*$ is some positive number (around ~2.8). I'm looking for a way to determine $p^*$ and to prove the inequality for $p$ greater than this threshold. Any suggestions on approaches or relevant theorems would be greatly appreciated.

Thank you!

For which $p>p^*$ does the inequality $\rm{cos}^2(−π/4+π/p)>1/2+π/p^2$​ hold?

I have the inequality $\rm{cos}^2(−\frac{\pi}{4}+\frac{\pi}{p})>\frac{1}{2}+\frac{π}{p^2}$​​ and have found that it holds for $p>p^*$, where $p^*$ is some positive number (around ~2.8). I'm looking for a way to determine $p^*$ and to prove the inequality for $p$ greater than this threshold. Any suggestions on approaches or relevant theorems would be greatly appreciated.

Thank you!

For which $p>p^*$ does the inequality $\cos^2(−π/4+π/p)>1/2+π/p^2$​ hold?

I have the inequality $\cos^2(−\frac{\pi}{4}+\frac{\pi}{p})>\frac{1}{2}+\frac{π}{p^2}$​​ and have found that it holds for $p>p^*$, where $p^*$ is some positive number (around ~2.8). I'm looking for a way to determine $p^*$ and to prove the inequality for $p$ greater than this threshold. Any suggestions on approaches or relevant theorems would be greatly appreciated.

Thank you!

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blockchain_dietmar
blockchain_dietmar
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For which $p>p^*$ does the inequality $\rm{cos}^⁡2^2(−π/4+π/p)>1/2+π/p^2$​ hold?

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blockchain_dietmar
blockchain_dietmar
  • 11
  • 3

For which $p>p^*$ does the inequality $\rm{cos}^⁡2(−π/4+π/p)>1/2+π/p^2$​ hold?

I have the inequality $\rm{cos}^2(−\frac{\pi}{4}+\frac{\pi}{p})>\frac{1}{2}+\frac{π}{p^2}$​​ and have found that it holds for $p>p^*$, where $p^*$ is some positive number (around ~2.8). I'm looking for a way to determine $p^*$ and to prove the inequality for $p$ greater than this threshold. Any suggestions on approaches or relevant theorems would be greatly appreciated.

Thank you!