# General Solution

1. Oct 5, 2005

### 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?

2. Oct 5, 2005

### amcavoy

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

3. Oct 5, 2005

### cscott

I feel dumb for asking now

0 + pi * k

4. Oct 5, 2005

### amcavoy

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

Alex

5. Oct 5, 2005

### cscott

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

Last edited: Oct 5, 2005
6. Oct 5, 2005

### TD

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

7. Oct 5, 2005

### cscott

Thank you kind sirs.

8. Oct 6, 2005

### TD

You're welcome