Consider the circle c of radius 7, centered at the origin. (a) find a parametrization for c inducing a counterclockwise orientation and starting at (7, 0). c(t) = , 0 ≤ t ≤ 2π (b) find a parametrization for c inducing a clockwise orientation and starting at (0, 7). c(t) = , 0 ≤ t ≤ 2π (c) find a parametrization for c if it is now centered at the point (4, 3). c(t) = , 0 ≤ t ≤ 2π

We have a circle of radius 7, centered at the origin, so we need to find a parametrization for c as follows:

Part (a) 

As shown in figure 1,  c is inducing a counterclockwise orientation, so using trigonometry the equations are given by:



As:



if then and  that is the condition for the problem.

Part (b) 

As shown in figure 2,  c is inducing a clockwise orientation, so using trigonometry the equations are given by:



As:



if then and  that is the condition for the problem.

Part (c) 

As shown in figure 3,  c is now centered at the point (4, 3). Let's assume that it is inducing a counterclockwise orientation, so using trigonometry and doing a displacement of 4 in x-axis and 3 in y-axis, the equations are given by:



Where: