Question
Show that the curve with parametric equations $x=t \cos t$ $y=t \sin t, z=t$ lies on the cone $z^{2}=x^{2}+y^{2},$ and use this fact to help sketch the curve.
Step 1
We have $x=t \cos t$, $y=t \sin t$, and $z=t$. Substituting these into the equation of the cone $z^{2}=x^{2}+y^{2}$, we get $t^{2}=(t \cos t)^{2}+(t \sin t)^{2}$. Show more…
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