# convert space curve to cartesian

by yanyin
Tags: cartesian, convert, curve, space
 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
 P: 661 x= sint, y=sqrt(2)cost, z=sint u can clearly see that x2 + y2 +z2=2{sin2t +cos2t} =2 x2 + y2 +z2=2
 Sci Advisor HW Helper P: 9,398 And eqaully clearly, surely you can see there is more to it than that? You've just replaced a locally 1-d structure (a curve) with a locally 2-d 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 $$x=z=(1-y^2)^{1/2}/\sqrt 2$$
P: 21

## convert space curve to cartesian

 Originally posted by matt grime And eqaully clearly, surely you can see there is more to it than that? You've just replaced a locally 1-d structure (a curve) with a locally 2-d 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 $$x=z=(1-y^2)^{1/2}/\sqrt 2$$
Thanks matt grime, i've checked yours is correct.
but can you show me how the above equation is reached.
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,706 If matt grime will forgive me for sticking in my oar: x= sint, y=sqrt(2)cost, z=sint so obviously x= z. x2= sin2t= (1-cos2t). But y2= 2 cos2t so cos2t= y2/2. That is x2= 1- y2/2 and x= z= √(1- y2/2).

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