Question

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

Answer 1

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)`