   Chapter 10.1, Problem 3E

Chapter
Section
Textbook Problem

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.3. x = t + sin t, y = cos t, −π ≤ t ≤ π

To determine

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

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=t+sint (1)

The parametric equation for the variable y is as follows.

y=cost (2)

The range of t is π to π .

Calculation:

The value of t is increased from π to π with a step value of π2 and substituted in the Equations (1) and (2) to obtain the value of x and y , respectively.

Substitute π for t in the Equation (1).

x=π+sin(π)=π+0x=π

Substitute π for t in the Equation (2)

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