Question

What is the polar form of `( -34,99 )`?

Answer 1

`(104.676, 1.902)`

Explanation:

We're asked to find the polar coordinate of a given Cartesian coordinate.

To do this, we can use the the equations

`ul(r^2 = x^2 + y^2`

`ul(theta = arctan(y/x)`

for the polar coordinate `(r,theta)`

Here,

`x = -34`

`y = 99`

So we have

`r^2 = (-34)^2 + 99^2`

`r = sqrt((-34)^2 + 99^2) = color(red)(ulbar(|stackrel(" ")(" "104.676" ")|)`

The argument `theta` will be

`theta = arctan(99/(-34)) = ul(-1.240)` OR `ul(1.902` (both in radians)

Arctangent calculations will give two answers, each a half-circle (`pi`/`180^"o"`) apart, so be sure to know which one it is.

Here, the `x`-coordinate is negative and the `y`-coordinate is positive, so the angle must be in quadrant II (i.i. the angle must be betwen `pi/2` and `pi`).

Thus,

`color(red)(ulbar(|stackrel(" ")(" "theta = 1.902" ")|)`

So the polar coordinate is

`color(blue)((104.676, 1.902)`