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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