Problem 3E

Give a set of parametric equations that describes a full circle of radius R, where the parameter varies over the interval [0, 10].

Solution 3E

Step 1:

A circle can be defined as the locus of all points that satisfy the equations

and

where x,y are the coordinates of any point on the circle, r is the radius of the circle and

t is the parameter - the angle suspended by the point at the circle's center.

Therefore the parametric equation of a circle can be written as

where