   Chapter 10.1, Problem 13E

Chapter
Section
Textbook Problem

# (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 the parameter increases. 13. x = sin t, y = csc t, 0 < t < π/2

(a)

To determine

To obtain: A Cartesian equation of the curve by eliminating parameter t .

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=sint (1)

The parametric equation for the variable y is as follows.

y=csct

y=1sint (2)

The range of t is 0 to π2 .

Calculation:

Substitute sint=x in the equation (2) ,

y=1x

For the time interval

(b)

To determine

To plot: The curve using the parametric equations. x=sint and y=1sint .

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