Find the Parametrization for the Curve $x ^ { 2 } + y ^ { 2 } = 6$

question 8

Multiple Choice

Find the parametrization for the curve.
-The portion of the circle $x ^ { 2 } + y ^ { 2 } = 6$ that lies in the second quadrant

• A) \(x = 6 \sin t , y = 6 \cos t\), for \(\pi < t < \frac { 3 \pi } { 2 }\)
• B) \(x = 6 \cos t , y = 6 \sin t\), for \(\frac { \pi } { 2 } < t < \pi\)
• C) \(x = 6 \cos t , y = 6 \sin t\), for \(\frac { 3 \pi } { 2 } < t < 2 \pi\)
• D) \(x = 6 \sin t , y = 6 \cos t\), for \(\frac { \pi } { 2 } < t < \pi\)

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Definitions:

Independent Variable

A variable in an experiment or model that is manipulated or categorized to observe its effect on the dependent variable.

Dependent Variable

In an experimental setting, the variable being tested and measured, which is expected to change as a result of modifications to the independent variable.

Independent Variables

Variables in an experiment that are manipulated to determine if they cause a change in the dependent variable.

Observations

The individual entities or datapoints collected for research or analysis purposes, providing the basis for statistical conclusions.