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Find a parametrization of the circle of radius [radius] in the xy-plane, centered at the origin, oriented clockwise. The point should correspond to [point]. Use [parameter] as the parameter for all of your answers.

User Booth
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Final answer:

A clockwise parametrization of a circle in the xy-plane with radius 'radius' is given by (radius cos(parameter), -radius sin(parameter)). Specific values for 'radius', 'point', and 'parameter' are needed to provide an exact parametrization.

Step-by-step explanation:

To parametrize a circle of radius radius, centered at the origin and oriented clockwise in the xy-plane, we use trigonometric functions. Typically, a counter-clockwise parametrization of a circle with radius r is given by (r cos(t), r sin(t)), where t is the parameter that represents the angle in radians from the positive x-axis. However, for a clockwise orientation, we switch the sign of the sine component to reflect the reverse direction of travel around the circle. Thus, a clockwise parametrization can be expressed as (r cos(parameter), -r sin(parameter)).

Assuming [radius] is the numeric value of the radius, [point] is a specific point on the circle, and [parameter] is the variable used as the parameter, the parametrization would specifically depend on these given values. Without the numeric values, the exact parametrization cannot be detailed further.

Note that in this context, radius does not refer to a variable, but rather is a placeholder for the actual length of the radius that should be specified in the parametrization. Similarly, point and parameter are placeholders that would be replaced with the specific values given in the problem.

User Krn
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