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(a) Eliminate the parameter to find a Cartesian equation of the curve.

(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as parameter increases.

$ x = \sin t $, $ \quad y = \csc t $, $ \quad 0 \leqslant t \leqslant \pi/2 $

(a) $x=\sin t, y=\csc t, 0<t<\frac{\pi}{2}, y=\csc t=\frac{1}{\sin t}=\frac{1}{x}$

For $0<t<\frac{\pi}{2},$ we have $0<x<1$ and $y>1 .$ Thus, the curve is

the portion of the hyperbola $y=1 / x$ with $y>1$

(b) Graph

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Jorge R.

April 27, 2018

this is incorrect

Jorge R.

April 27, 2018

It should be y= (1/x) b/c Csc(t)= 1/(sin(t)), Csc(t) = y and Sin(t) = x getting y= (1/x)

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