Answer:
a) [tex]x=a\cdot cos(b), y=-a\cdot sin(b), 0 \leq b \leq 2\pi[/tex]
b) [tex]x=a\cdot cos(b), y=a\cdot sin(b), 0 \leq b \leq 2\pi[/tex]
c) [tex]x=a\cdot cos(b), y=-a\cdot sin(b), 0 \leq b \leq 6\pi[/tex]
d) [tex]x=a\cdot cos(b), y=a\cdot sin(b), 0 \leq b \leq 6\pi[/tex]
Step-by-step explanation:
The parametric equation for a circle is:
[tex]x=a\cdot cos(b)[/tex]
[tex]y=a\cdot sin(b)[/tex]
Where a is the radius and b is the angular displacement.
a) If a is negative in y and 0 ≤ b ≤ 2π, we have clockwise moves.
[tex]x=a\cdot cos(b), y=-a\cdot sin(b), 0 \leq b \leq 2\pi[/tex]
b) If a is positive in y and 0 ≤ b ≤ 2π, we have counterclockwise moves.
[tex]x=a\cdot cos(b), y=a\cdot sin(b), 0 \leq b \leq 2\pi[/tex]
c) If a is negative in y and 0 ≤ b ≤ 6π, we have three times clockwise moves.
[tex]x=a\cdot cos(b), y=-a\cdot sin(b), 0 \leq b \leq 6\pi[/tex]
d) If a is positive in y and 0 ≤ b ≤ 6π, we have three times counterclockwise moves.
[tex]x=a\cdot cos(b), y=a\cdot sin(b), 0 \leq b \leq 6\pi[/tex]
Have a nice day!
