Question

What is the Cartesian form of `( -9 , ( - 15pi)/2 )`?

Answer 1

(0. -9)

Explanation:

We have the coordinate `(-9, (-15pi)/2)` in polar form.

Coordinates in polar form have the standard form `(color(green)(r), color(purple)(Θ))`.

To convert from polar form to Cartesian form, we use the following formulas:

• `color(red)(x) = color(green)(r)coscolor(purple)(Θ)`
• `color(blue)(y) = color(green)(r)sincolor(purple)(Θ)`

Now, let's plug stuff in. We know `color(green)(r) = -9` and `color(purple)(Θ) = (-15pi)/2`

`color(red)(x) = (-9)*cos((-15pi)/2)`

`color(red)(x) = (-9)*(0)`

`color(red)(x) = 0`

`color(blue)(y) = (-9)*sin((-15pi)/2)`

`color(blue)(y) = (-9)*(1)`

`color(blue)(y) = -9`

We get `color(red)(x) = 0` and `color(blue)(y) = -9`, making our Cartesian coordinate `(0, -9).`