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 \((x,y)\).