x=sint y=csct 0<t<pi/2

Question

given the parametric equations

eliminate the parameter to find cartesian equation of the curve

sketch the curve and indicate orientation

Answer 1

Notice that x y = sint csct = 1

That is y = 1 /x. 0< x <1 and 0< y <1

Now about the orientation since the graph lies in the fist quadrant the hyperbola y = 1 /x

the y's start at −∞ dropping to 1.