The Cartesian coordinates of a point are given. (i) Find polar coordinates (r,θ) of the point, where r&gt;0and0≤θ&lt;2π. (ii) Find polar coordinates (r,θ) of the point, where r&lt;0 and 0≤θ&lt;2π. (33,3)

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The Cartesian coordinates of a point are given.  (i) Find polar coordinates (r,θ) of the point, where r&amp;gt;0and0≤θ&amp;lt;2π.  (ii) Find polar coordinates (r,θ) of the point, where r&amp;lt;0 and 0≤θ&amp;lt;2π. (33,3)

Alannej · Accepted Answer

Here given rectangular coordinate (x,y)=(33,3) which is in First Quadrant Now use the relation r=x2+y2 we need to find out value of r&amp;gt;0 r=(33)2+32=6 The angle θ is given by θ=tan−1(yx)=tan−1(333) θ=tan−1(13) Since the point is in first quadrant and tan⁡π6=13 we will consider θ=π6 Polar coordinate for r&amp;gt;0 is (r,θ)=(6,π6) Other representation of r&amp;lt;0 are P(r,θ)=P(r,θ+(2n+1)π) (−6,π6+π)=(−6,7π6)   add π Result: (6,π6) and (−6,7π6)

The Cartesian coordinates of a point are given. (i) Find polar coordinates (r

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