Homework Help: Method of differentials

1. Aug 30, 2006

Sethka

I am completly lost on these differentials! Can anyone help me make sense of them? Especially this question in particular:

cot(46(deg))

(Sorry, I don't know how to make that small little circle thing that denotes degree)

I'm supposed to use the method of differentials to estimate it to 4 decimal places.

Thanks!

2. Aug 30, 2006

StatusX

Show what you've tried. Do you know how to use this method?

By the way, I'd never heard of the "method of differentials" before, and I had to do a google search to figure out what it is. It seems to just be synonomous with "linear approximation", or, if you want a higher order approximation, "taylor series approximation", by which names I think the method is much more well known. Just another reason to always show your work if you want help.

3. Aug 30, 2006

HallsofIvy

45 degrees is $\frac{\pi}{4}$ radians. 1 degree is $\frac{\pi}{180}$ radians. It's better to use radians because that way the derivative is easier: if x is measured in radians then the derivative of y= cos(x) is y'= -sin(x) and so the differential is dy= -sin(x)dx. y+ dy= cos(x)- sin(x)dx.
To find $cos(\frac{pi}{4}+ \frac{\pi}{180}$, let $x= \frac{\pi}{4}$ so that $y= cos(\frac{\pi}{4})= \frac{\sqrt{2}}{2}$, $-sin(x)= -sin(\frac{\pi}{4})= -\frac{\sqrt{2}}{2}$ and $dx= \frac{\pi}{180}$.

4. Aug 30, 2006

Sethka

Oh Thanks!

Thanks you guys, My text books are a little backwards it seems. Where one asks me to use method of differentials the other teaches linear aproximation, that was so confusing and now I see why. Thanks A bunch!