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anonymous
 one year ago
A curve in polar coordinates is given by: r=8+2cosθ.
Point P is at θ=18π/16.
(1) Find polar coordinate r for P, with r>0 and π<θ<3π/2
r=
(2) Find cartesian coordinates for point P.
x= , y=
anonymous
 one year ago
A curve in polar coordinates is given by: r=8+2cosθ. Point P is at θ=18π/16. (1) Find polar coordinate r for P, with r>0 and π<θ<3π/2 r= (2) Find cartesian coordinates for point P. x= , y=

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3it is the same procedure, we have to substitute this: \[\Large \begin{gathered} x = r\cos \theta \hfill \\ \hfill \\ {x^2} + {y^2} = {r^2} \hfill \\ \end{gathered} \]

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2to get the value of r, since P lies on that curve, you can plug in \(\theta = 18\pi/16 \) in \(r= 8+2 \cos \theta \)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3\[\Large r = 8 + 2\cos \left( {\frac{{9\pi }}{8}} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3furthermore, we have to use this formula: \[\Large y = r\sin \theta \] for ycoordinate

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3and, of course: \[\Large \theta = \frac{{18\pi }}{{16}} = \frac{{9\pi }}{8}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so what is (Find cartesian coordinates for point P. ) x= , y=

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2we have r and \(\theta\) \(x = r\cos \theta \\ y = r \cos \theta \)
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