Now, the cosecant of θ is -6, or namely -6/1.
however, the cosecant is really the hypotenuse/opposite, but the hypotenuse is never negative, since is just a distance unit from the center of the circle, so in the fraction -6/1, the negative must be the 1, or 6/-1 then.
we know the cosine is positive, and we know the opposite side is -1, or negative, the only happens in the IV quadrant, so θ is in the IV quadrant, now

recall that

therefore, let's just plug that on the remaining ones,

now, let's rationalize the denominator on tangent and secant,
If you would like to know whether or not what she wrote is accurate, it is.
Hope that helps!
We simply replace a with -9
k(-9) = 4 * -9 - 4
k(-9) = -40
:)
All you have to do is multiply it then you get the answer