Question

Let C be the curve given by r(t) = <tcos(t), tsin(t), t>. a) Show that C...

Let C be the curve given by r(t) = <tcos(t), tsin(t), t>.

a) Show that C lies on the cone x^2 + y^2 = z^2 and draw a rough sketch of C on the cone.

b) Use a computer algebra system to plot the projections onto the xy- and yz-planes of the curve r(t) = <tcos(t), tsin(t).

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Answer #1

Then for lying on this curve, we have

So that and we can say that the curve lies on the cone

Cone (3D surface) with the curve C (in dotted green) is shown below

b) Projections in XY plane are of the form given below:

Projection in YZ plane is of the form which is given below:

Made in Desmos

Please do rate this answer positively if you found it helpful. Thanks and have a good day!

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