[tex]\Large\boxed{\begin{array}{l}\sf sen\bigg(\dfrac{7\pi}{2}\bigg)\cdot cos\bigg(31\pi\bigg)\\\sf \dfrac{7\pi}{2}=\dfrac{4\pi}{2}+\dfrac{3\pi}{2}=2\pi+\dfrac{3\pi}{2}\\\\\sf sen \bigg(\dfrac{7\pi}{2}\bigg)= sen\bigg(\dfrac{3\pi}{2}\bigg)=-1\\\\\sf 31\pi=15\cdot2\pi+\pi\\\sf cos(31\pi)=cos(\pi)=-1\\\sf sen\bigg(\dfrac{7\pi}{2}\bigg)\cdot cos(31\pi)=(-1)\cdot(-1)=1\end{array}}[/tex]