Chapter 4.6, Problem 81PE

Given $r\left(x\right)=-x^2,s\left(x\right)=\cot x,$ and $t\left(x\right)=\csc x$ ,

a. Find $\left(r\circ t\right)\left(x\right)$

b. Graph $s\left(x\right)$ and $\left(r\circ t\right)\left(x\right)$ together on the ZTRIG window. The relationship between the two graphs will be studied in calculus. For a given value of $x$ in the domain of $s\left(x\right)=\cot x,y=-{\csc }^{2}x$ gives the slope of a line tangent to $s$ at $x$ .