Find a rectangular equation for the plane curve defined by t

Find a rectangular equation for the plane curve defined by the parametric equations

Solution

we know (cost)^2 + (sint)^2 = 1

so given x = 3 sint and y = 3 cost 0 <= t <= 2 pi

x^2 + y^2 = (3 sint )^2 + 3 cost )^2

===> 9 sin^2t + 9 cos^2t

===> 9 (sin^2t + cos^2t)

==> 9

therefore

x^2 + y^2 = 9

this is rectangualr curve : x^2 + y^2 = (3)^2

it is circle with radius of 3