## 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=

1. Michele_Laino

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

2. hartnn

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

3. Michele_Laino

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

4. Michele_Laino

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

5. Michele_Laino

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

6. anonymous

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

7. hartnn

we have r and $$\theta$$ $$x = r\cos \theta \\ y = r \cos \theta$$