To find the equation of the tangent line, we need to find the slope via the derivative. We can either apply the quotient rule or the power rule (by recognising
. Using the quotient rule:
This gives:
At
, we have
(from part (a)), and so that means that the slope of the curve at
is
We will also need the
-value at the point
(here we used the fact that the function
is
periodic and then applied the computation from part (a)).
This means our tangent line is: