   Chapter 13.1, Problem 7E

Chapter
Section
Textbook Problem

# Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases.7. r(t) = ⟨sin t, t⟩

To determine

To sketch: the curve of vector equation r(t)=sint,t and indicate the direction of increment of t.

Explanation

Definition:

Consider a vector function as r(t)=f(t),g(t) , then parametric equations to plot space curve C are,

x=f(t)y=g(t)

Here,

f(t) and g(t) are component functions of r, and

x, and y are parametric equations of C.

From definition, write the parametric equations for vector function r(t)=sint,t .

x=sinty=t

Consider a certain interval of t as (2π,2π) to plot the vector equation.

The estimated values of x and y in the interval (2π,2π) are shown in Table 1

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