General Solution

[cscott]

For the general solution of sin x = 0, must you have a solution using 0, pi and 2pi (ie. pi + 2pi * k, 2pi + 2pi * k, ...) or does using pi suffice?

[amcavoy]

For the general solution of sin x = 0, must you have a solution using 0, pi and 2pi (ie. pi + 2pi * k, 2pi + 2pi * k, ...) or does using pi suffice?
Sin(x) is zero when x is 0, pi, 2pi, etc. What does this tell you in terms of writing a general solution? Pay attention to the coefficients.

Alex

[cscott]

I feel dumb for asking now

0 + pi * k

[amcavoy]

I feel dumb for asking now

0 + pi * k
Yes, for all non-negative integer values of k.

Alex

[cscott]

Yes, for all non-negative integer values of k.

Alex

Doesn't it still work for negative integers or am I missing something?

[TD]

For the general solution of sin x = 0, must you have a solution using 0, pi and 2pi (ie. pi + 2pi * k, 2pi + 2pi * k, ...) or does using pi suffice?
If you use k*pi with k an integer, you have all of your solutions.
Since, choose k = 0 to find the solution 0, use k = 1 to find the solution pi and use k = 2 to find 2*pi. Of course, all (positive and negative) multiples or 2*pi are allowed as well :smile:

[cscott]

Thank you kind sirs.

[TD]

You're welcome :smile: