Question

Cot y, if csc y =-10/3 and cos y< 0

Answer 1

`\csc y=-\frac{10}3\implies\sin y=-\frac3{10}`


`\cos^2y=1-\sin^2y\implies \cos y=\pm\sqrt{1-\frac9{100}}=\pm(√(91))/(10)`

You're told that
`\cos y<0`, so omit the positive root.


`\cot y=(\cos y)/(\sin y)=\frac{-(√(91))/(10)}{-\frac3{10}}=\frac{√(91)}3`