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:
[tex]\left \{ {{x=7cost} \atop {y=7sint}} \right.[/tex]
As:
[tex]t \in [0, 2 \pi ][/tex]
if [tex]t=0[/tex] then [tex]x=7[/tex] and [tex]y=0[/tex] 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:
[tex]\left \{ {{x=7sint} \atop {y=7cost}} \right.[/tex]
As:
[tex]t \in [0, 2 \pi ][/tex]
if [tex]t=0[/tex] then [tex]x=0[/tex] and [tex]y=7[/tex] 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:
[tex]\left \{ {{x=7cost+4} \atop {y=7sint+3}} \right.[/tex]
Where:
[tex]t \in [0, 2 \pi ][/tex]
