Question

Find cot theta if csc theta =-sqrt37/6 and tan theta>0

Answer 1

\[\sin^2(x)+\cos^2(x)=1 \\ \text{ divide both sides by } \sin^2(x) \\ 1+\cot^2(x)=\csc^2(x) \\ 1+(\cot(x))^2=(\csc(x))^2 \\ \]

Answer 2

replace csc(x) with -sqrt(37)/6
and then solve for cot(x)

Answer 3

and yes I changed your theta to x

Answer 4

keep in mind if tangent is positive then so is cotangent
so you will take the positive answer

Answer 5

Thank you!

Answer 6

np