How do you find all polar coordinates of point P where P = (7, pi/3)?

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How do you find all polar coordinates of point P where P = (7, pi/3)?

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Answer 1 · 2015-11-11T14:00:08

If $P$ $P$ has Cartesian coordinates $(7, \frac{π}{3})$ $(7,pi/3)$ then its Polar coordinates are
$(\sqrt{7^{2} + {(\frac{π}{3})}^{2}}, arctan (\frac{π}{21}))$ $(sqrt(7^2+(pi/3)^2), arctan(pi/21))$

Explanation:

The given coordinates $(7, \frac{π}{3})$ $(7,pi/3)$ look as if they are already in polar form (radius $= 7$ $=7$ , and angle $= \frac{π}{3}$ $=pi/3$ ).
but in case $(7, \frac{π}{3})$ $(7,pi/3)$ really are Cartesian coordinates (i.e. $(x, y) = (7, \frac{π}{3})$ $(x,y) =(7,pi/3)$ )

The radius is given by $\sqrt{x^{2} + y^{2}}$ $sqrt(x^2+y^2)$ and
the angle by $arctan (\frac{y}{x})$ $arctan(y/x)$

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How do you find all polar coordinates of point P where P = (7, pi/3)?

1 Answer

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