Question 882836
One of the 6 trigonometric function values, {{{highlight(sin(theta)=-1/3))}}} , is given.
{{{(cos(theta))^2+(sin(theta))^2=1}}}
{{{(cos(theta))^2+(-1/3)^2=1}}}
{{{(cos(theta))^2+1/9=1}}}
{{{(cos(theta))^2=1-1/9}}}
{{{(cos(theta))^2=8/9}}} ---> {{{system(cos(theta)=sqrt(8/9),"or",cos(theta)=-sqrt(8/9))}}}
Since {{{cos(theta)<0}}} ,
{{{cos(theta)=-sqrt(8/9)}}}-->{{{cos(theta)=-sqrt(8)/sqrt(9)}}}-->{{{highlight(cos(theta)=-2sqrt(2)/3))}}}
{{{csc(theta)=1/sin(theta)}}}-->{{{csc(theta)=1/(-1/3)}}}-->{{{csc(theta)=1*(-3/1)}}}-->{{{highlight(csc(theta)=-3)}}}
{{{sec(theta)=1/cos(theta)}}}-->{{{sec(theta)=1/(-2sqrt(2)/3)}}}-->{{{sec(theta)=-3/2sqrt(2)}}}-->{{{sec(theta)=-3sqrt(2)/2sqrt(2)sqrt(2))}}}-->{{{highlight(sec(theta)=-3sqrt(2)/4)}}}
{{{tan(theta)=sin(theta)/cos(theta)}}}
{{{tan(theta)=(-1/3)/(-2sqrt(2)/3)}}}-->{{{tan(theta)=(-1/3)*(-3/2sqrt(2))}}}-->{{{tan(theta)=1/2sqrt(2))}}}-->{{{tan(theta)=1*sqrt(2)/2sqrt(2)sqrt(2))}}}-->{{{highlight(tan(theta)=sqrt(2)/4))}}}
{{{cot(theta)=cos(theta)/sin(theta)}}}
{{{cot(theta)=(-2sqrt(2)/3)/(-1/3)}}}-->{{{cot(theta)=(-2sqrt(2)/3)*(-3)}}}-->{{{highlight(cot(theta)=2sqrt(2)))}}}