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 $z = t$. The cone equation is $z^2 = x^2 + y^2$. Substituting the parametric equations into the cone equation gives us $t^2 = (t \cos t)^2 + (t \sin t)^2$. Show more…
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