Question

• plot All points of intersections (for 2 equations) that have been determined graphically (label points) Written as polar coordinates• All points of intersections (for same 2 equations) that have been determined algebraically

Answer 1

Solution

I will pick the two graphs

$\begin{gathered} r=4cos3\theta \\ and \\ r=4cos\theta \end{gathered}$

Their point of intersection on the graph is

That is the point

$\begin{gathered} r=4 \\ \theta=0\degree \end{gathered}$

To solve algrebrically, we have

$\begin{gathered} 4cos3\theta=4cos\theta \\ \\ cos3\theta=cos\theta \\ \\ Equating\text{ the argument} \\ \\ 3\theta=\theta \\ \\ 2\theta=0 \\ \\ \theta=0\degree \\ and\text{ } \\ \\ r=4cos\theta \\ \\ r=4cos(0) \\ \\ r=4 \end{gathered}$

The polar coordinate is

$(r,\theta)=(4,0)$