Question

Find the value of cot(x) if sec(x)=-9/2 , sin(x)<0

Answer 1

`\sec x=-\frac92\implies\cos x=-\frac29`


`\sin^2x+\cos^2x=1\implies\sin x=\pm√(1-\cos^2x)`

`\sin x<0\implies\sin x=-√(1-\left(-\frac29\right)^2)=-\frac{√(77)}9`


`\cot x=(\cos x)/(\sin x)`

`\implies\cot x=\frac{-\frac29}{-\frac{√(77)}9}=\frac2{√(77)}`