Tangent's ratio is, as we all know, Cosine/Sine, which relates to the reason to why it has asymptotes. Sine has the possibility of having the value of 0, make the ratio undefined, creating an asymptote in the graph. According to the Unit Circle, Sine is positive in the I and II quadrants, Cosine is positive in the I and IV quadrants and Tangent is positive in the I and III quadrants. Cotangent is but the reciprocal of Tangent, meaning that the ratio is Sine/Cosine. Cotangent is also another that includes an asymptote in it's graph because of the undefined ratio solution.
Secant is the reciprocal of Cosine, meaning the ratio is R/X giving it an asymptote if the x (cosine) is equal to 0.
Cosecant is the reciprocal of Sine, meaning that the ratio is R/Y giving it an asymptote if the y (sine) is equal to 0
According to this graph, there are no asymptotes present, but it does give a small interpretation of how the Unit Circle unfolds onto a graph. the loop going up is divided in half and the first half is the first quadrant and the second half is the second quadrant, so on and so on. these quadrants represent the value of the sign that the trig functions have in the graph.
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