Does this negative sign even matter in sin(x)?

[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

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)

 

[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.

 

[chroot]

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

 

[mr_coffee]

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

 

[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.

 

[Hurkyl]

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.