Question

Number 2 please, what did I do wrong?

Answer 1

see explanation

Explanation:

To convert from rectangular to polar coordinates, that is

(x, y ) → (r, Θ )

r =
`√(x^2+y^2)`

Θ =
`tan^(-1)`(
`(y)/(x)`)

Given (-
`√(3)`, - 1 ), then

r =
`\sqrt{(- [tex]√(3)`)^2 + (-1)^2

=
`√(3+1)`

=
`√(4)` = 2 and

Θ =
`tan^(-1)`(
`(-1)/(-√(3) )` =
`tan^(-1)`(
`(1)/(√(3) )` = 30°

The rectangular coordinate point is in the third quadrant, thus Θ must be in the third quadrant, that is

Θ = 180° + 30° = 210°

Thus (r, Θ ) = (2, 210° )