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)