# Homework Help: Does this negative sign even matter in sin(x)?

1. Feb 27, 2006

### mr_coffee

Hello everyone, when i'm doing these problems i always make sure i put a negative inside the sin(x) function, then just later take it out like
cos(2t)+sin(-2t) = cos(2t)-sin(2t); Because sin is an odd function.
But my professor says f it and never does, for instance here is my work, i came out with the professors answer but he didn't use the negative at all, he just acted as if it was r1 = -9+2i, r2 = -9+2i, rather than r1,2 = -9+/- 2i;
http://suprfile.com/src/1/2dq85j/lastscan.jpg [Broken]

He does this with all his problems, even in an e-mail, he told me, don't worry about putting the negative sign inside the sin function. So is this true?

THe professors answer was:
y = e^(-9t)(18sin(2t)+3cos(2t))
which is the same as mine once i take that negative sign out of the sin(x)

Last edited by a moderator: May 2, 2017
2. Feb 27, 2006

### KingNothing

Well, sin(x) is different from sin(-x). There are some problems where it will make a difference and some where it won't.

3. Feb 27, 2006

### chroot

Staff Emeritus
Since sin(x) is not an even function, sin(x) = sin(-x) for only some specific values (namely, x = k*pi), but not in general.

- Warren

4. Feb 27, 2006

### mr_coffee

so when dealing with Differential equations should i stlil toss it in there or just do it like my professor?

5. Feb 27, 2006

### KingNothing

Definitely leave it in there. For the equations you deal with right now, it might be removable, but you don't want to develop bad habits for when it does matter.

6. Feb 27, 2006

### Hurkyl

Staff Emeritus
If B is an arbitrary constant, then so is -B.

Anyways, you should review the theorem that allows you to solve these types of differential equations in this way, and see what it has to say about it.