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(a) (4 3 , 4)
(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) =
(ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) =
(b) (1, −3)
(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) =
(ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) =

Respuesta :

raphealnwobi

Answer:

The answer is below

Step-by-step explanation:

A point in the coordinate plane can either be represented using the Cartesian form or the polar corm. The Cartesian form is represented as (x, y) where x and y are the horizontal and vertical coordinates while the polar form is represented as (r, θ), θ is the angle and r is the length.

Conversion of (x, y) to (r, θ) is:

[tex]r=\sqrt{x^2+y^2}\\ \\\theta=tan^{-1}(\frac{y}{x} )[/tex]

a) (3, 4)

[tex]r=\sqrt{3^2+4^2}=5\\ \\\theta=tan^{-1}\frac{4}{3}=53.13^o=0.295\pi[/tex]

(3, 4) = (5, 0.296π)

b) (1, -3)

[tex]r=\sqrt{1^2+(-3)^2}=\sqrt{10} \\ \\\theta=tan^{-1}\frac{-3}{1}=1.6\pi[/tex]

(3, 4) = (√10, 1.6π)

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