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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 isthe portion of the hyperbola $y=1 / x$ with $y>1$(b) Graph

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JR

Jorge R.

April 27, 2018

this is incorrect

JR

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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### Video Transcript

the problem is part of a eliminated the permitted to find a Kardashian question out the curve. So for about a half x squire us long over why Square is he called to sign his squire Asco. Sign his squire. But you see what I want. This is a petition question off the curve. I'd be scratch the curve and indicated with an error or two different direction in which the crew fits interest as permitted increases. There's a curve is the like one teensy could've zero with half Mexican. Who, Cyril and why is equal to one. So here one tea increases have axe increases, and why also increases? So it's like, Yeah, and what Axe approaches pi over, too we have. Why approaches to infinity. This area is the direction in which the curve is trist as permitting increases.

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#### Topics

Parametric Equations

Polar Coordinates

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