   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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