# Thread: a cone equation

1. ## a cone equation

Show that r(t)=tsin(pi*t)i + tj +tcos(pi*t)k lies on a cone, find the equation for this cone and sketch it.

How should I solve this question? Thank you very much.

2. Originally Posted by Jenny20
Show that r(t)=tsin(pi*t)i + tj +tcos(pi*t)k lies on a cone, find the equation for this cone and sketch it.

How should I solve this question? Thank you very much.
Convert it to coordinate form:

x = t sin(pi*t)

y = t

z = t cos(pi*t)

Now eliminate t:

x^2+z^2= t^2 [sin^2(pi*t) + cos^2(pi*t)] = t^2 = y^2

or:

x^2 + z^2 = y^2

which is a cone with its axis horizontal.

RonL

3. thank you !