Find parametric equations for the path of a particle that moves along the circle x2 + (y - 3)2 = 16 in the manner described.

Question

 (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.)
1)once around clockwise, starting at (4,3) 0≤t≤2pi
2)three times around counter clockwise, starting at (4,3) 0≤t≤6pi
3)halfway around counter clockwise, starting (0,7) 0≤t≤pi.

I am unsure what form its asking for and where to start? 

Answer 1

Jon,

        Again it best to make a rough sketch and label the points on the circle and the coordinate axis. Note the center of the circle is located at (0,3) and has a radius of 4 units.

 

         A point (x,y) on the circle can be located by x=4*cos(t), y=3+4*sin(t) where the parameter (angle) is >=0 and <=2pi radians This is the answer to part 1) above. when t=0 x=4 and y=3. Clockwise movement.

 

          Part 2 requires the point move counterclockwise so all you have to do is change the sign of the argument . So the equations become x=4*cos(t) and y=(3-4*sin(t)) as t goes from 0 to 6pi radians. since cos(-t)=cos(t) and sin(-t)=-sin(t)

 

          You give part 3 a try ok

 

Jim