Integers n satsifying \frac{1}{\sin \frac{3\pi}{n}}=\frac{1}{\sin \frac{5\pi}{n}}

Alvin Pugh

Alvin Pugh

Answered question

2022-01-24

Integers n satsifying 1sin3πn=1sin5πn

Answer & Explanation

primenamaqm

primenamaqm

Beginner2022-01-25Added 12 answers

Let πn=x and equation is sin5x=sin3x
From sin5x=sin3x you get either
5x=3x+2kπ
or
5x=π3x+2kπ
The former yields x=kπ, so 1=kn, whence n=±1.
The latter yields
πn=182k+1π
that is, (2k+1)n=8. Hence n=±8

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?