X= sin(t), y = csc(t), 0 < t < π/2 (a) eliminate the parameter to find a cartesian equation of the curve.

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

A Cartesian equation of the curve is 
   y = 1/x . . . . . -1 ≤ x ≤ 1

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.