What are the polar coordinates?

Answer 1

What are polar coordinates of (√2, 1)?

Solution:

Here we need to convert from rectangular coordinates to polar coordinates:

P = (x, y) = (r, θ)

r = ± √(x^2 + y^2); tan θ = y/x or θ = arc tan (y/x)

So we have:

P = (√2, 1)

r = ± √[(√2)^2 + 1^2] = ± √3

θ = arc tan (y/x) = arc tan (1/√2) = arc tan (√2/2) ≈ 35.3°, which is one possible value of the angle.

(√2, 1) is in the Quadrant I. If θ = 35.3°, then the point is in the terminal ray, and so r = √3.

Therefore polar coordinates are (√3, 35.3°).

Another possible pair of polar coordinates of the same point is (-√3, 215.3°)

(180° + 35.3° = 215.3°).

Edit: Note the negative in the r value.