Q. 1TB Parametric equations for the uni... [FREE SOLUTION]

Chapter 11: Q. 1TB (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 counterclockwise once on the interval[0, 2蟺] starting at the point (1, 0).

Short Answer

Expert verified

The parametric equation for the unit circle centered at the origin of thexy-plane that satisfy the given condition is $\begin{array}{r} x = \cos t \\ y = \sin t \end{array}\} 0 鈮� t 鈮� 2 蟺 .$

Step by step solution

Step 1. Given Information.

It is given that the unit circle is centered at the origin and the graph is traced counterclockwise with a starting point $(1, 0) .$

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, $x^{2} + y^{2} = 1 and (x, y) = (0, 0) .$

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

localid="1649645222370" $x (t) = co s t y (t) = \sin t$

Now, the graph is traced counterclockwise once with a starting pointlocalid="1649645297884" $(1, 0),$

localid="1649646331434" $x (t) = \cos t y (t) = \sin t$

Thus, the parametric equation of the circle is:

$\begin{array}{r} x = \cos t \\ y = \sin t \end{array}\} 0 鈮� t 鈮� 2 蟺 .$

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91影视

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 counterclockwise once on the interval[0, 2蟺] starting at the point (1, 0).

Short Answer

Step by step solution

Step 1. Given Information.

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

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

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 counterclockwise once on the interval[0, 2蟺] starting at the point (1, 0).

Short Answer

Step by step solution

Step 1. Given Information.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Calculus

Discrete Mathematics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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 counterclockwise once on the interval[0, 2蟺] starting at the point (1, 0).