Parametrizing a Circle - Concept

Concept Concept (1)

One application of parametric equations that is useful to learn is how to parameterize a circle. In order to parameterize a circle centered at the origin, oriented counter-clockwise, all we need to know is the radius. In order to understand how to parameterize a circle, it is necessary to understand parametric equations, and it can be useful to learn how to parameterize other figures, such as line segments.

Sample Sample Problems (3)

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Parametrizing a Circle - Problem 1
Problem 1
How to find parametric equations of a semicircle centered at (0,0) with radius 12, oriented counter-clockwise.
Parametrizing a Circle - Problem 2
Problem 2
How to find parametric equations of a circle centered at (3,4) with radius 5, oriented counter-clockwise.
Parametrizing a Circle - Problem 3
Problem 3
How to write the parametric equations of a circle or semicircle centered at (0,0) with radius r, oriented clockwise.