Problem $2$: Using rise functions $[10$ points$]$

The following rise function is proposed for a rise$-$dwell$-$fall$-$dwell motion program.

s$(\backslash$theta $)=5[(\backslash$theta $)/(\backslash$beta $)-(1)/(2\backslash$pi $)$sin$(2\backslash$pi $(\backslash$theta $)/(\backslash$beta $))]$

where $\backslash$beta is the rise interval in degree, s is in mm $,$ and $\backslash$theta is in degree.

a$\backslash$theta $=0\backslash$deg $,\backslash$theta $=90\backslash$deg $,\backslash$theta $=135\backslash$deg and $\backslash$theta $=270\backslash$deg $.$

c