Question

how to solve cot[arcsin(-sqrt2/9)]

Answer 1

cot=cos/sin
sin^2+cos^2=1
cos=sqrt(1-sin^2)
cot=sqrt(1-sin^2)/sin

Answer 2

1) Please draw a right triangle.
2) Designate an angle.
3) Label two sides so that the sine of that angle is \(\sqrt{2}/9\)
4) Use the Pythagorean Theorem to find the length of the third side.
5) The cotangent should now be trivial - almost.
6) The original sine was negative. This is Quadrants III and IV. You will have to figure out the correct sign of the cotangent you seek.