Question

For each question, the rectangular coordinates of a point are given. Find the polar coordinates of each point.

4. (4, 0)

5. (3, 4)

6. (2, -2)

Answer 1

(r, theta) can be found by
r^2=x^2+y^2
tan(theta) = y/x

Answer 2

let's do the first...
r^2 = 4^2+0^2 ---> r^2 = 16 ---> r = 4
tan(theta) = 0/4 ---> tan(theta) = 0 ---> theta = 0

(4, 0) rectangular is (4, 0) in polar

Answer 3

5. Polar ( r, θ ) = ( 5, 53°)
r = √(3² + 4²) = 5
θ = arctan ( 4/3) = 53°

Similarly,
6. ( 2√2, -45° )