Question

eliminate the parameter to find the cartesian equation of the curve for x=sin(t), y=csc(t), 0<t<pi/2

Answer 1

We can start by using the identity csc(t) = 1/sin(t) to eliminate the parameter t:

y = csc(t)
y = 1/sin(t)
sin(t) = 1/y
x = sin(t) = 1/y

Therefore, the cartesian equation of the curve is x*y = 1.