Question
Show that the curve with parametric equations x=tcost, y=tsint, z=t lies on the cone z^2=x^2+y^2
Answers
Damon
x^2 = t^2 cos^2
y^2 = t^2 sin^2
x^2 + y^2 = t^2(cos^2+sin^2) = t^2
but t^2 = z^2
so
x^2+y^2 = z^2
y^2 = t^2 sin^2
x^2 + y^2 = t^2(cos^2+sin^2) = t^2
but t^2 = z^2
so
x^2+y^2 = z^2