Convert space curve to cartesian

1. Feb 14, 2004

yanyin

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. Feb 15, 2004

himanshu121

x= sint, y=sqrt(2)cost, z=sint

u can clearly see that
x2 + y2 +z2=2{sin2t +cos2t}

=2

x2 + y2 +z2=2

3. Feb 15, 2004

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 $$x=z=(1-y^2)^{1/2}/\sqrt 2$$

4. Feb 15, 2004

yanyin

Thanks matt grime, i've checked yours is correct.
but can you show me how the above equation is reached.

5. Feb 15, 2004

HallsofIvy

Staff Emeritus
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