Answer
a)
$y=\frac{1}{x}$
$0 \lt x \lt 1$
b)
The arrow must point such that: x increases as t increases.
Work Step by Step
a)
First equation:
$x=sin t$
Second equation:
$y=csc t= \frac{1}{sin t}$
because by definition,
$csc t = \frac{1}{sint}$
Replace $sin t$ with $x$ (from the first equation).
We get
$y=\frac{1}{x}$
$0 \lt t \lt \frac{π}{2}$
$sin(0)=0$
$sin(\frac{π}{2})=1$
Therefore,
$0 \lt x \lt 1$
And because $y=\frac{1}{x}$
We have $y \gt \infty$
b)
Draw graph of $y=\frac{1}{x}$, where $0 \lt x \lt 1$
There is a hole at (1 ,1) because $x=1$ is not in the domain and because $t=\frac{\pi}{2}$ is not in the domain.
And $sin t$ increases as $t$ increases.
Therefore, the arrow must point such that: x increases and y decreases as t increases.
