Cartesian coordinates are represented as the ordered pair, (x, y)(x,y), and can be converted to polar coordinates, represented as (r, theta)(r,θ), using the following three identities.
x=rcos(theta)x=rcos(θ)
y=rsin(theta)y=rsin(θ)
r=sqrt(x^2 + y^2)r=√x2+y2
Lets start by finding rr. Plugging xx and yy into the identity for rr yields;
r = sqrt(5^2 + 0^2) = sqrt(5^2) = 5r=√52+02=√52=5
If we plug xx and rr into the first identity, we get;
5 = 5cos(theta)5=5cos(θ)
5/5 = cos(theta)55=cos(θ)
1= cos(theta)1=cos(θ)
On the unit circle, cos(0) = 1cos(0)=1, so theta = 0θ=0. Our ordered pair is therefore;
(r, theta) = (5, 0)(r,θ)=(5,0)
