consider the following.\n\n$x = \\sin(t),\\ y = \\csc(t),\\ 0 < t < \\frac{\\pi}{2}$\n\n(a) eliminate the…

Explanation:

Step1: Recall the reciprocal relation

We know that $\csc(t)=\frac{1}{\sin(t)}$.

Step2: Substitute the given parametric - equations

Given $x = \sin(t)$ and $y=\csc(t)$. Since $\csc(t)=\frac{1}{\sin(t)}$, substituting $x$ for $\sin(t)$ and $y$ for $\csc(t)$ into the relation, we get $y=\frac{1}{x}$. Also, since $0\lt t\lt\frac{\pi}{2}$, for $x = \sin(t)$, we have $0\lt x\lt1$, and for $y=\csc(t)$, we have $y > 1$.

Answer:

$y=\frac{1}{x},0\lt x\lt1,y > 1$