Explanation Given information: x = − sin t and the Cartesian equation of the semicircle is x = 1 − y 2 , − 1 ≤ y ≤ 1 Definition: Parametric equations are a way to encode the movement of the particle along the curve. Calculation: Given that: x = 1 − y 2 , − 1 ≤ y ≤ 1 x = − sin t x = 1 − y 2 ⇒ x 2 = 1 − y 2 ⇒ 1 − x 2 = y 2 ⇒ y = 1 − x 2 Substituting x = − sin t in the line equation y = 1 − x 2 , we get y = 1 − ( s i n t ) 2 y = 1 − s i n 2 t y = cos 2 t y = cos t Therefore, the set of parametric equations are: x = − sin t y = cos t Since, − 1 ≤ y ≤ 1 , − 1 ≤ cos t ≤ 1 − 1

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Author: Ratti

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Chapter 8.7, Problem 53E

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A set of parametric equations and interpret the motion of a particle moving along the right semicircle of radius 1 whose Cartesian equation is x=1−y2,−1≤y≤1 by using the parameter t with −∞<t<∞.

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Chapter 8.7, Problem 52E

Chapter 8.7, Problem 54E

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Chapter 8 Solutions

Precalculus: A Unit Circle Approach

Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E

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A set of parametric equations and interpret the motion of a particle moving along the right semicircle of radius 1 whose Cartesian equation is x = 1 − y 2 , − 1 ≤ y ≤ 1 by using the parameter t with − ∞ < t < ∞ .

Solution Summary: The author explains that parametric equations encode the motion of a particle along the right semicircle of radius 1 by using the parameter t with -infty.

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To find:

A set of parametric equations and interpret the motion of a particle moving along the right semicircle of radius 1 whose Cartesian equation is x=1−y2,−1≤y≤1 by using the parameter t with −∞<t<∞.

Want to see the full answer?

Chapter 8 Solutions

A set of parametric equations and interpret the motion of a particle moving along the right semicircle of radius 1 whose Cartesian equation is x = 1 − y 2 , − 1 ≤ y ≤ 1 by using the parameter t with − ∞ &lt; t &lt; ∞ .

Solution Summary: The author explains that parametric equations encode the motion of a particle along the right semicircle of radius 1 by using the parameter t with -infty.

Videos

To find: A set of parametric equations and interpret the motion of a particle moving along the right semicircle of radius 1 whose Cartesian equation is x=1−y2,−1≤y≤1 by using the parameter t with −∞<t<∞.

Want to see the full answer?

Chapter 8 Solutions

A set of parametric equations and interpret the motion of a particle moving along the right semicircle of radius 1 whose Cartesian equation is x = 1 − y 2 , − 1 ≤ y ≤ 1 by using the parameter t with − ∞ < t < ∞ .

To find:

A set of parametric equations and interpret the motion of a particle moving along the right semicircle of radius 1 whose Cartesian equation is x=1−y2,−1≤y≤1 by using the parameter t with −∞<t<∞.