SOLUTION: 2sec(t)tan(t) + sec^(2)(t) What (if any) are the zeros, holes, and vertical asymptotes?

Question 393007: 2sec(t)tan(t) + sec^(2)(t)
What (if any) are the zeros, holes, and vertical asymptotes?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The expression could be written as .
Find out first the values of t where the top is equal to the bottom, i.e., :

==> , or sint(2 + sint) = 0.
==> sint = 0 ==> t =0, +/-, +/- , +/- ,...
At these t values the bottom, is not equal to zero. The top, is also not equal to 0 (it is equal to 1). Therefore there are no "holes" in the graph.
There are vertical asymptotes at t values where = 0, namely
t = +/-, +/- , +/- ,...
The x-intercepts are located at t = +/- and t = +/- . (These are the t values where 2sint + 1 = 0).
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