Question 1089973
{{{sin(x)}}},{{{ cos(x)}}},{{{ sec(x)}}},{{{ csc(x)}}} all have a period of {{{2pi}}} so,
{{{-(9/4)pi+2pi=(-9/4+8/4)pi=-pi/4}}}

So, 
{{{sin(-(9/4)pi)=sin(-pi/4)=-sin(pi/4)=-sqrt(2)/2}}}
Since,
{{{csc(-pi/4)=1/sin(-pi/4)}}}
Then,
{{{csc(-pi/4)=-2/sqrt(2)=-sqrt(2)}}}
So,
{{{highlight_green(csc(-(9/4)pi)=-sqrt(2))}}}