Question

Let n be a fixed positive integer. Describe all solutions of sin(n theta) = 1/2

I know that the solutions would be
(π/6)/n+(2πx)/n
and
(5π/6)/n+(2πx)/n
?

How do I 'describe'

Answer 1

It looks like a communication question

Answer 2

the period is 2π/n

so, the solutions are

π/6n + k(2π/n) = π/6n (12k+1)
5π/6n + k(2π/n) = π/6n (12k+5)
for all integers k.