Question

What is the Cartesian form of `(-10,(-17pi)/16))`?

Answer 1

`(15.693, -3.121)`

Explanation:

We're asked to find the Cartesian (rectangular) form of a given polar coordinate.

To do this, we use the equations

`ul(x = rcostheta`

`ul(y = rsintheta`

In this case,

• `r = -10`

• `theta = (-17pi)/16`

So we have

`x = -16cos((-17pi)/16) = ul(15.693`

`y = -16sin((-17pi)/16) = ul(-3.121`

The Cartesian coordinate is thus

`color(blue)(ulbar(|stackrel(" ")(" "(15.693, -3.121)" ")|)`