Question 732705
{{{cot(theta)=cos(theta)/sin(theta)}}}
Let's find {{{x=sin(theta)}}}
If {{{x=sin(theta)}}} then {{{cos(theta)=sqrt(1-x^2)}}} and
{{{cot(theta)=sqrt(1-x^2)/x}}} so {{{sqrt(1-x^2)/x=-3/4}}}
and squaring both sides we get {{{(1-x^2)/x=(-3/4)^2}}} --> {{{(1-x^2)/x=9/16}}}
{{{(1-x^2)/x^2=9/16}}} --> {{{1/x^2-1=9/16}}} --> {{{1/x^2=1+9/16}}} --> {{{1/x^2=25/16}}} --> {{{x^2=16/25}}} --> {{{x=-4/5}}} or {{{x=4/5}}}
But since {{{cos(theta)>0}}} and {{{cot(theta)=cos(theta)/sin(theta)=-3/4<0}}}
{{{sin(theta)<0}}} so {{{x=highlight(sin(theta)=-4/5)}}}