Calculus help? ?

Question

i really do not understand how to do this problem. it was on a test and i do not remember learning it. now we have to make corrections to the test as a homework assignment and i still am confused. explanations don't help much but seeing the problem worked usually helps me teach myself and i need to know for the make up test on friday. please help me

x=4cos(t) y=4sin(t) 0≤t≤2π

initial point

terminal point

Answer 1

This is a parametric equation, parameterized by the variable t.

It's initial point is when t=0: (x,y)=(4,0)

and it's terminal point is when t=2*pi: (x,y)=(4,0).

The points are the same because it's actually the equation of a circle. The equation could be rewritten as

x^2+y^2=16.