anonymous
  • anonymous
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=
Mathematics
jamiebookeater
  • jamiebookeater
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Michele_Laino
  • Michele_Laino
it 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
  • hartnn
to 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
  • Michele_Laino
\[\Large r = 8 + 2\cos \left( {\frac{{9\pi }}{8}} \right)\]

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Michele_Laino
  • Michele_Laino
furthermore, we have to use this formula: \[\Large y = r\sin \theta \] for y-coordinate
Michele_Laino
  • Michele_Laino
and, of course: \[\Large \theta = \frac{{18\pi }}{{16}} = \frac{{9\pi }}{8}\]
anonymous
  • anonymous
so what is (Find cartesian coordinates for point P. ) x= , y=
hartnn
  • hartnn
we have r and \(\theta\) \(x = r\cos \theta \\ y = r \cos \theta \)

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