Question

how do you write x^2+y^2=5 in polar coordinates?

Answer 1

\[\huge x = r \cos \theta , y = r \sin \theta\]

Answer 2

thanks :)

Answer 3

how do i get it to be r^2=something?

Answer 4

\[\huge r = \sqrt{x^2 + y^2}\]

Answer 5

When converting to polar,

x = r cos theta
y = r sin theta

Plug in x and y

(r cos theta) ^ 2 + (r sin theta) ^2 = 5

r^2 * (cos theta)^2 + r^2 * (sin theta) ^2 = 5

factor out r^2

r^2 (cos theta ^2 + sin theta ^ 2) = 5

We see this trig identity cos theta ^2 + sin theta ^2 = 1

so r^2 (1) = 5

thus, r = sqrt(5)

Hope this helped.

Answer 6

It did :) thanks!