   Chapter 10.1, Problem 8E

Chapter
Section
Textbook Problem

# (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b) Eliminate the parameter to find a Cartesian equation of the curve. 8. x = sin t, y = 1 − cos t, 0 ≤ t ≤ 2π

(a)

To determine

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

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=1cost (2)

The range of t is 0 to 2π .

Calculation:

The value of t is increased from 0 to 2π with a step value of 1 and substituted in the parametric Equations (1) and (2) to obtain the value of x and y respectively.

Substitute 0 for t in Equation (1).

x=sint=sin(0)x=0

Substitute 0 for t in Equation (2).

y=1cost=1cos(0)=11y=0

The values of x and y for each step value of t is tabulated in the below table

(b)

To determine

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

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