Question

What is the Cartesian form of `( -2 , ( - 9pi)/2 )`?

Answer 1

The Cartesian point is `(0,2)`

Explanation:

Given: `r = -2 and theta = (-9pi)/2`

For the x coordinate, use the equation:

`x = rcos(theta)`

`x = -2cos((-9pi)/2)`

`x = 0`

For the y coordinate, use the equation:

`y = rsin(theta)`

`y = -2sin((-9pi)/2)`

`y = 2`

The Cartesian point is `(0,2)`

Answer 2

`( 0 , 2 )`

Explanation:

It can be seen from the diagram that the x coordinate of P is `rcos(theta)` and the y coordinate of P is `rsin(theta)`

So:

`x=rcos(theta)`

`y=rsin(theta)`

From example:

`x=-2cos((-9pi)/2)= 0`

`y=-2sin((-9pi)/2)=2`

Cartesian coordinate:

`( 0 , 2 )`