Please help with Trig question, not a homework.

[yungman]

This is part of the derivation in EM theory. I try to simplify and be very specific. I don't agree with the book but this book usually is accurate:

I need to find:

$$cos (\frac {n\pi}{2} + \frac {n\pi x}{2}) \;\hbox { where }\; n= 1,3,5...$$

The usual way to solve this is:

$$cos (A+B) = cos A cos B - sin A sin B$$

$$\Rightarrow \; cos (\frac {n\pi}{2} + \frac {n\pi x}{2}) = cos (\frac {n\pi}{2}) cos ( \frac {n\pi x}{2}) - sin (\frac {n\pi}{2}) sin ( \frac {n\pi x}{2})$$

$$\Rightarrow \; cos (\frac {n\pi}{2} + \frac {n\pi x}{2}) = - sin (\frac {n\pi}{2}) sin ( \frac {n\pi x}{2}) \;\hbox { because }\; cos (\frac {n\pi}{2}) = 0$$

$$sin (\frac {n\pi}{2}) = 1 \hbox { for } \;n=1,\;\;\; sin (\frac {n\pi}{2}) = -1 \;\hbox { for } \; n=3,\;\;\; sin (\frac {n\pi}{2}) = 1 \;\hbox { for }\; n=5.$$

Therefore the answer change sign with different n. But the book gave:

$$cos (\frac {n\pi}{2} + \frac {n\pi x}{2}) = -sin (\frac {n\pi x}{2})$$

There is no sign change according to the book. What am I missing? Please help.

Thanks

Alan

 

[chiro]

I can't see any errors in your work.

One possibility is to check either the authors website or the publishers website for the errata (basically errors and their fixes). If there is a mistake (and often if there is people send in emails or if its used in a classroom its quickly found out), then that is your best bet in seeing if this error has been called on by someone else.

 

[yungman]

Thanks, that's what I want to hear. This is very obvious to me! But I just never have enough confidence to say it.