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Converting intrinsic coordinates to cartesian

I searched the for a method... but it didnt work out (didnt make sense to me)

Was doing a past pper and came acrross the question:

Y = LN (SEX X)

how would you convert back to cartesian from here??

many thanks

Reply 1

James

I don't get it. That looks Cartesian to me, provided that the Sex function is well-defined. :rolleyes:

Reply 2

DFranklin

James Gurung

I don't get it. That looks Cartesian to me, provided that the Sex function is well-defined. :rolleyes:

Well, it's usually 1-1 and onto, at any rate...

Reply 3

James

DFranklin

Well, it's usually 1-1 and onto, at any rate...

Lol! I haven't heard that one before. :biggrin:

Reply 4

redbuthotter

ooops i meant cartesian to intrinsic and yea there are limits... its pi over 3 and pi over 2

Reply 5

James

I haven't done this for ages, but here's my attempt...

If

y=\ln(\sec x)

then

\frac{\mathrm{d}y}{\mathrm{d}x}=\tan(x)

.

But in intrinsic coordinates, we have

\frac{\mathrm{d}y}{\mathrm{d}x}=\tan(\psi)

Therefore I guess you can put

x=\psi

.

Now

\frac{\mathrm{d}x}{\mathrm{d}s}=\cos(\psi)=\cos(x)

\frac{\mathrm{d}s}{\mathrm{d}x}=\sec(x)

.

Thus

s=\ln(\sec(\psi)+\tan(\psi))

.

That's probably wrong. My method seems a bit dodgy. Tbh I need to revise this stuff.

Reply 6

insparato

You're forgetting the C.

I did this with the definition of

S = \sqrt{1+\left(\frac{dy}{dx}\right)^2}

Got a different answer hmm.

Why are there limits? Surely if you're being asked to convert cartesian into intrinsic, limits wouldnt come into play with this?

Reply 7

James

Yeah you're right. I really can't remember any of this stuff.

Reply 8

redbuthotter

would you say dy/dx is tan(w) and if so isnt it always tan(w)?? because by defintion dy/dx = tan(w) this is the bit that confuses me.

Reply 9

insparato

Yes but because d/dx(ln secx) = tanx

dy/dx = tan x

dy/dx = tan w

therefore w= x

Reply 10

redbuthotter

so if it was a different equiation would dy/dx not = w

Reply 11

insparato

dy/dx doesnt equal w it equals tan w and it is infact tan x as well.

dy/dx = tanx - because the function when differentiated is tanx

dy/dx = tanw - As you know by definition of an intrinsic equation

So in this special case x = w

If it was a different function then this would not be the case. You'd then have to find a relationship between x = w.

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