Question

Plato Question!!!!

Type the correct answer in each box.
What is a polar form of (-1, √3 ) is ( _ , _ ) ?

Answer 1

Explanation:

Answer:

Explanation:

The polar form of a Cartesian coordinates is given by (r, @) where r = √x^2 + y^2

@ = tan^-1 y/x

r = √-1^2 + √3^2

r = √4

r= 2

@ = tan ^-1 √3/-1 -tan √3/1 = -60°

@ = 180-60 = 120°

Answer 2

(2, 120° )

Explanation:

To convert from rectangular to polar form, that is

(x, y) → (r, Θ ), use

r =
`√(x^2+y^2)`

Θ =
`tan^(-1)`(
`(y)/(x)`)

here (x, y ) = (- 1,
`√(3)`)

r =
`\sqrt{(-1)^2+(√(3) }` )^2

=
`√(1+3)` =
`√(4)` = 2

Θ =
`tan^(-1)`(
`√(3)`) = 60° ← related acute angle

Note (- 1,
`√(3)`) is in the second quadrant so Θ must be in the second quadrant.

Θ = 180° - 60° = 120°

(- 1,
`√(3)`) → (2, 120°)