Find the Exact Value cot(arctan(-3/5))

Draw a triangle in the plane with vertices ${\displaystyle (1,-\frac{3}{5})}$, ${\displaystyle (1,0)}$, and the origin. Then ${\displaystyle \arctan (-\frac{3}{5})}$ is the angle between the positive x-axis and the ray beginning at the origin and passing through ${\displaystyle (1,-\frac{3}{5})}$. Therefore, ${\displaystyle \cot \left(\arctan (-\frac{3}{5})\right)}$ is ${\displaystyle -\frac{5}{3}}$.