Question

Change these rectangular coordinates to polar coordinates: (3, -3). Give answer in degrees and simplify radicals if necessary?

Answer 1

`color(purple)((r,theta) = (4.2426, 135^@)` or `color(purple)((4.2426, 315^@)`

Explanation:

Given : `(x,y) = (3, -3)`

`r = sqrt(x^2 + y^2)`

`r = sqrt(3^2 + (-3)^2) = sqrt18 = 3sqrt2 = 4.2426`

`tan theta = y / x = -3/3 = -1`

`theta = tan ^-1 (-1) = tan-^-1 tan(180 -45) = 135^@` or `tan^-1(-45 )= 315^@`

`color(purple)((r,theta) = (4.2426, 135^@)` or `color(purple)((4.2426, 315^@)`