What is the Cartesian form of #( 4, (5pi)/2 ) #?

1 Answer
Jul 17, 2016

The point is #(0,4)#.

Explanation:

The standard conversion between polar and cartesian coordinates is:
#x = r cos(theta)#
#y = r sin(theta)#

The given coordinates are of the form #(r, theta)#. And one will also note that:
#(5pi)/2 = pi/2 + 2pi#

Meaning that we can simply reduce the angle to #pi/2# since we can always subtract full revolutions of the unit circle from angles in polar coordinates, so the result is:
#x = 4cos((pi)/2) = 0#
#y = 4sin((pi)/2) = 4#

The point, then, is #(0,4)#