Estimating cot(46°) Using Method of Differentials

[Sethka]

I am completely 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!

 

[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.

 

[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 $dx= \frac{\pi}{180}$.

 

[Sethka]

Oh Thanks!

Thanks you guys, My textbooks 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!