Choose the rectangular coordinates for the polar coordinate (6, 2pi).?

Question

Im looking how to set up this problem and get the answer..
I know the answer is either...
a) (0, 6)
b) (0, -6)
c) (6, 0)
d) (-6, 0)

Thanks for any help..

Answer 1

1 pi is half circle so 2pi is 1 full circle, that's moving counterclockwise from the x axis in the first quadrant.
a -pi (negative pi) moves clockwise starting from the x axis in the first quadrant.
Therefore, 2pi moving counterclokwise at full circle , will stop at the origin, 0. So (6,2pi ) is at point (6,0)

Answer 2

Polar coordinates are given in the form (r, Theta), where r is the radius from the origin (0,0), and theta is the rotation, in radians, counter-clockwise, where theta=0 being the 3 on a clock face.

The radius here is 6, so we start at (6,0) then rotate theta.

Since 2pi radians corresponds to 360 degrees, we've gone once around the clock, and are back at (6,0). The solution is (c).

Answer 3

Those others are all correct saying (6,0).

Remember that the angle is measured anticlockwise from the positive x-axis.

Also 2pi (in radians) is equivalent to 360 degrees, so this means a full turn ie back at the positive x-axis.

Answer 4

2pi is one complete circle, so this polar coordinate is back on the x-axis. This would be at +6 on the x-axis, or c) (6,0)

Answer 5

if x,y are the cartesian coordinates
the corresponding polar r,z
then the relations are
r^2=x^2+y^2
tanz=y/x
we therefore write the equations
x^2+y^2=36
tan2pi=y/x
y/x=0
x can not equal to zero
so y=0
x=6 from the first eqn.
answer
6,0
c)

Answer 6

2Pi is 360 degrees. So the answer is (6,0).

Answer 7

the anwser is a because 2pi is a complete circle puting you back on the x-axis.

Answer 8

(6 cos(2pi) , 6 sin(2pi))=(6,0)