Polar Coordinates and Equations

    1. Plot each point given in polar coordinates.    SOLUTION

     (a) $\left(4, \frac{3\pi}{4}\right)$              (b)  $\left(3, -\frac{\pi}{6}\right)$               (c) $\left(-2, \frac{\pi}{2}\right)$   

    2. Which quadrant does the the following point lie in?    SOLUTION

     (a)  $(r,\theta)=\left(-1,-\dfrac{7\pi}{6}\right)$          (b)     $(r,\theta)=\left(-2,\dfrac{5\pi}{6}\right)$ 

   3. Perform each indicated conversion. Answer using exact values.   SOLUTION

     (a) Convert $(x,y)=(2,-2)$ to polar coordinates $(r,\theta)$ such that $r>0$ and $0\leq \theta < 2\pi$.

     (b) Convert $(r,\theta)=\left(-3, -\frac{3\pi}{4}\right)$ to rectangular coordinates $(x,y)$.

    4. Perform each indicated conversion. Answer using exact values.     SOLUTION

    (a) Convert $(x,y)=(0, 7)$ to polar coordinates $(r,\theta)$ such that $r>0$ and $0\leq \theta < 2\pi$.

    (b) Convert $(r,\theta)=\left(3, \frac{5\pi}{6}\right)$ to rectangular coordinates $(x,y)$.