Question 1099073
You have an angle, {{{theta}}} that has
{{{system(cot(theta)=(-3/4), csc(theta)=(5/4))}}} .
All the trigonometric functions can be calculated from sine and cosine.
{{{csc(theta)=1/sin(theta)}}} , so you have {{{1/sin(theta)=5/4}}} ---> {{{highlight(sin(theta)=4/5)}}}
 
{{{cot(theta)=cos(theta)/sin(theta)}}} , so you have {{{cos(theta)/sin(theta)=-3/4}}} , or {{{cos(theta)/((4/5))=-3/4}}} ---> {{{cos(theta)=(-3/4)*(4/5)}}} ---> {{{highlight(cos(theta)=-3/5)}}} .
 
To complete the half-dozen trigonometric functions, the other two are
{{{sec(theta)=1/cos(theta)}}} and {{{tan(theta)=sin(theta)/cos(theta)}}} or {{{tan(theta)=1/cot(theta)}}} , so
 
{{{sec(theta)=1/(-3/5)}}} ---> {{{highlight(sec(theta)=-5/3)}}} , and
 
{{{tan(theta)=1/(-3/4)}}} ---> {{{highlight(tan(theta)=-4/3)}}} .
 
{{{drawing(300,300,-5,2,-2,5,
grid(1),red(circle(0,0,1)),
red(arrow(0,0,-3.6,4.8)),
red(arc(0,0,3.1,3.1,-126.7,0)),
red(triangle(-0.9,1.2,-0.7,1.2,-0.9,1.4)),
locate(0.56,1.7,red(theta))
)}}}