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Chapter 11: Q. 2TB (page 859)

Parametric equations for the unit circle: Find parametric equations for the unit circle centered at the origin of the xy-plane that satisfy the given conditions.

The graph is traced clockwise once on the interval[0, 2π] starting at the point (1, 0).

Short Answer

Expert verified

The parametric equation for the unit circle centered at the origin of the xy-plane that satisfies the given condition isx(t)=costy(t)=-sint0≤t≤2π.

Step by step solution

01

Step 1. Given Information.

It is given that the unit circle is centered at the origin and the graph is traced clockwise once with a starting point1,0.

02

Step 2. Find the parametric equation for the unit circle. 

It is given that the circle is centered at the origin and it is a unit circle. Thus,

x2+y2=1andx,y=0,0.

Now, the parametric equation of a circle of center 0,0and radius 1is:

x(t)=costy(t)=sint

Now, the graph is traced clockwise once with a starting point1,0:

x(t)=costy(t)=-sint

Thus, the parametric equation of the circle is:

x(t)=costy(t)=-sint0≤t≤2π.

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Most popular questions from this chapter

Find parametric equations for each of the vector-valued functions in Exercises 26–34, and sketch the graphs of the functions, indicating the direction for increasing values of t.

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