Looking at this question again, I don't understand why you're told "for y=11". That doesn't seem relevant at all... So you can disregard the answer I posted a few minutes ago on your other question.
a) With , differentiate both sides with respect to
to get
b) The point P occurs at , which corresponds to a
-coordinate of
The slope of the line tangent to this point is approximately
so the equation of the tangent line is approximately
c) The tangent line to the graphed curve is vertical when is undefined. This happens when
, or
and
where
is any integer.
In case you're not sure where the general solution came from: We have
which has an infinite number of solutions. is one of them, which we obtain by taking the inverse sine of both sides of this equation. Since
, we also know that
is a solution. And since
for integers
, we also know that we can add any multiple of
to these two solutions to get infinitely more solutions.
