Parametric Equations and And a Parameter Interval for the Motion $x=2 \cos t, y=2 \sin t, \pi \leq t \leq 2 \pi$

question 256

Multiple Choice

Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph
traced by the particle and the direction of motion.
- $x=2 \cos t, y=2 \sin t, \pi \leq t \leq 2 \pi$

• A) \(x ^ { 2 } + y ^ { 2 } = 4\); Counterclockwise from \(( 2,0 )\) to \(( 2,0 )\), one rotation
• B) \(x ^ { 2 } + y ^ { 2 } = 4 ;\) Clockwise from \(( 2,0 )\) to \(( - 2,0 )\)
• C) \(x ^ { 2 } + y ^ { 2 } = 1\); Clockwise from\(( 1,0 )\) to \(( 1,0 )\)
• D) \(x ^ { 2 } + y ^ { 2 } = 4\); Counterclockwise from , one rotation \(( - 2,0 )\) to \(( 2,0 )\)

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Definitions:

Zero Slope

A horizontal line on a graph, indicating that there is no change in the y-value (vertical) regardless of the change in the x-value (horizontal); it represents a constant function.

Positive Slope

Indicates an upward trend on a graph, demonstrating that as one variable increases, the other variable also increases, especially used in the context of supply and demand curves in economics.

Consumption

The use of goods and services by households or individuals for personal needs or wants.

Income

Earnings received by an individual or entity, typically in the form of wages, salaries, or various types of investments.