Choose the polar coordinates for the rectangular coordinate? (sqrt2, 1)?

Question

Looking for the polar coordinates for the rectanglular coordinate
( Square root of 2, 1 )

I know it is one of the following answers

a. (sqrt2, 4.178)
b. (sqrt3, 0.615)
c. (-sqrt2, 2.095)
d. (2, 0.609)

Looking for answers to help me set up a problem like this one.

Answer 1

if you have a rectangular coordinate (x, y), the radius of the polar coordinate is the distance from the origin (0,0) to the point. The distance between two points (x1, y1) and (x2, y2) is (x2 -x1)^2 + (y2 - y1)^2 [where the notation is a^2 = a*a ].

To confirm it, note that the angle can be found from trigonometry, by noting that the tangent of an angle in a right triangle is the length of the opposite side over the length of the adjacent side, and that the y value of the point is the opposite side of the triangle formed by the origin, the point, and the point at (x, 0), while the x value of the point is the adjacent side: tan theta = y / x. (Draw the triangle to see what I mean). Then you can take inverse tangent of both sides to get the answer.

Answer 2

Cartesian coordinates are expressed as (x,y).

Polar coordinates are expressed as (r,θ)

where
x = rcos θ
y = rsin θ

r = √(x² + y²)
tan θ = y/x
θ = arctan(y/x)

r = √{(√2)² + 1²) = √(2 + 1) = √3
θ = arctan(1/√2) ≈ 0.615 radians

So the answer is b. (√3,0.615).

Answer 3

r=sqrt[x^2+y^2]
=sqrt[2+1]
=sqrt3
tanz=y/x=1/sqrt2
z=arctan.877
=41deg 15min
=.722
b.