When r = 0 then the angle can have any value.
When r > 0 then angles x and x+2kπ are the same for all integer values of k
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The point whose Cartesian coordinates are (2, 0) has the polar coordinates R = 2, Θ = 0 .
The trigonometric formula or the polar coordinate form is x = a + r*cosΦ y = b + r*sinΦ where 0 ≤ Φ < 360 deg.
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.
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account for the fact that some covalent bonds are polar while other are non-polar