[[☃ image 1]]
The four-petal flower $~r=2\sin(2\theta)~$ pictured above is graphed in polar coordinates on the interval $~\theta \in \left[\ 0,2\pi \right)\,$. If $~B~ $ is the point on the petal in Quadrant IV that is farthest from the pole (the origin), determine the polar coordinates of point $~B~$ and the exact slope of the tangent line to the curve at $~B\,$.
Coordinates of point $~B(r,\theta)~$: ( [[☃ expression 1]] , [[☃ expression 2]] )
Slope of tangent line at $~B~$: [[☃ input-number 1]]