Question

The letters r and θ represent polar coordinates. Write the following equation using rectangular coordinates (x, y).
Given equation r=5

Answer 1

huh? It's just a circle of radius 5!
r=5
r^2 = 25
x^2+y^2 = 25

Answer 2

Could you explain to me how? I wasn't school when the class was given and I am struggling a bit with it

Answer 3

you seem to recall that
x = r cosθ
y = r sinθ
How could you forget that
r^2 = x^2+y^2 ?
Just use the distance formula.
Or, if you insist on trig, recall that
x^2+y^2 = r^2 sin^2θ + r^2 cos^2θ = r^2 (sin^2θ + cos^2θ) = r^2

or, heck - read your math text. It explains it better then I can here, and surely with examples.