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Convert space curve to cartesian 
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#1
Feb1404, 08:58 PM

P: 21

if R = sinti+sqrt(2)costj+sintk, 0<=t<=Pi/2
please eliminate t to determine the cartesian equation of R(t). Put limits on the variables and verbally describe the curve 


#2
Feb1504, 02:48 AM

P: 658

x= sint, y=sqrt(2)cost, z=sint
u can clearly see that x^{2} + y^{2} +z^{2}=2{sin^{2}t +cos^{2}t} =2 x^{2} + y^{2} +z^{2}=2 


#3
Feb1504, 05:06 AM

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P: 9,396

And eqaully clearly, surely you can see there is more to it than that? You've just replaced a locally 1d structure (a curve) with a locally 2d structure, a sphere.
yes, the x, y, and z coordinates necessarily satisfy that, but that isn't sufficient. You need to intersect with the plane x=z (or similar) at the very least. generally the equation is [tex]x=z=(1y^2)^{1/2}/\sqrt 2[/tex] 


#4
Feb1504, 06:05 PM

P: 21

Convert space curve to cartesian
but can you show me how the above equation is reached. 


#5
Feb1504, 10:08 PM

Math
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Thanks
PF Gold
P: 39,345

If matt grime will forgive me for sticking in my oar:
x= sint, y=sqrt(2)cost, z=sint so obviously x= z. x^{2}= sin^{2}t= (1cos^{2}t). But y^{2}= 2 cos^{2}t so cos^{2}t= y^{2}/2. That is x^{2}= 1 y^{2}/2 and x= z= √(1 y^{2}/2). 


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