- #1
LmdL
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I have a trigonometric equation
[tex]2\sin \left ( \frac{q\pi }{m} \right )-\sin \left ( \frac{q\pi }{2} \right )=0[/tex]
and want to know what values m as a function of q could take to satisfy the equation. Both terms zero is the obvious solution: q=2n; m=2; n is an integer. But there are more solutions. I tried to use different kinds of trigonometric identities, with no luck.
The best I could get is
[tex]m=\frac{q\pi}{\arcsin \left ( \frac{1}{2}\sin \left ( \frac{q\pi }{2} \right ) \right )}[/tex]
which for q=2n gives q/m is an integer.
Is there a more elegant general solution?
Thanks!
[tex]2\sin \left ( \frac{q\pi }{m} \right )-\sin \left ( \frac{q\pi }{2} \right )=0[/tex]
and want to know what values m as a function of q could take to satisfy the equation. Both terms zero is the obvious solution: q=2n; m=2; n is an integer. But there are more solutions. I tried to use different kinds of trigonometric identities, with no luck.
The best I could get is
[tex]m=\frac{q\pi}{\arcsin \left ( \frac{1}{2}\sin \left ( \frac{q\pi }{2} \right ) \right )}[/tex]
which for q=2n gives q/m is an integer.
Is there a more elegant general solution?
Thanks!