Question

What is the polar form of `( -10,22 )`?

Answer 1

`(2sqrt146,1.998` `"rad")`

Explanation:

The polar form of the rectangular coordinate `(x, y)` can be found using these formulas:

`r = sqrt(x^2+y^2)`
`theta = tan^-1(y/x)`

So let's plug in the given x and y values.

`r = sqrt((-10)^2+22^2) = sqrt(100 + 484) = sqrt584 = 2sqrt146`

`theta = tan^-1(22/-10) = -1.144` `rad`

Now, since this point is in quadrant 2, and the angle produced by `tan^-1(y/x)` is in quadrant 4, we need to add `pi` `rad` to `theta` to get the correct angle.

So our polar coordinates are:

`(2sqrt146, 1.998)`

Final Answer