Q$6($b$).$ points $]$ Consider the state of stress on an element as shown below. Find the following:

$($i$)$ The principal stresses ${}_1$ and ${}_2,$ and the corresponding directions $($i$.$e$,$ angles ${}_{p1}$ and ${}_{p2}).$ What are the shear stress values in these directions? To receive full credit, you need to explain your answer.

$($ii$)$ The maximum in$-$plane shear stresses ${}_1$ and ${}_2,$ and the corresponding directions $($i$.$e$.,$ angles ${}_{s1}$ and ${}_{s2}).$ What are the associated normal stresses in these directions?

Note: You could use equations or Mohr Circle analysis. A graph paper is attached in case you want to solve it graphically or semi$-$graphically.