a. Tangent.
These graphs are different because we know that sin and cos are y/r and x/r so this is why neither of these graphs have asymptotes, r=1. Tangent on the other hand is y/x therefore wherever x or Cos is equal to zero, there is an asymptote.
b. Cotangent
Similar to tangent, cot is just x/y so wherever y or sin is equal to zero there is an asymptote, this is because the graph is undefined.
c. Secant
Because sec is r/x it will have asymptotes at the same places where tan had them but the two graphs look different because tan is only pi for a period and sec is relates to cos graph which is 2pi for a period.
d. Cosecant
Because csc is r/y it will have asymptotes at the same place where tan had them, and once again they are different because of the difference in the period length.
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