Question

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=

Answer 1

it is the same procedure, we have to substitute this:
\[\Large \begin{gathered}
x = r\cos \theta \hfill \\
\hfill \\
{x^2} + {y^2} = {r^2} \hfill \\
\end{gathered} \]

Answer 2

to get the value of r,
since P lies on that curve,
you can plug in \(\theta = 18\pi/16 \) in
\(r= 8+2 \cos \theta \)

Answer 3

\[\Large r = 8 + 2\cos \left( {\frac{{9\pi }}{8}} \right)\]

Answer 4

furthermore, we have to use this formula:
\[\Large y = r\sin \theta \]
for y-coordinate

Answer 5

and, of course:
\[\Large \theta = \frac{{18\pi }}{{16}} = \frac{{9\pi }}{8}\]

Answer 6

so what is (Find cartesian coordinates for point P. )
x= , y=

Answer 7

we have r and \(\theta\)

\(x = r\cos \theta \\ y = r \cos \theta \)