Question

Graph each pair of parametric equations
1.x=3 sin^3 t
y=3 cos^3 t

Answer 1

\[\frac{ x }{3 }=\sin ^{3}t,\]
taking cuberoot we get
\[\left( \frac{ x }{ 3 } \right)^{\frac{ 1 }{3 }}=\sin t\]
squaring both sides
\[\left( \frac{ x }{3 } \right)^{\frac{ 2 }{3 }}=\sin ^{2}t ...(1)\]
similarly \[\left( \frac{ y }{ 3 } \right)^{\frac{ 2 }{3 }}=\cos ^{2}t ...(2)\]
adding (1) & (2)
\[\left( \frac{ x }{3 } \right)^{\frac{ 2 }{3 }}+\left( \frac{ y }{3 } \right)^{\frac{ 2 }{ 3 }}=\sin ^{2}t+\cos ^{2}t=1\]
now you can make the graph.