A) Tangent
Tangent is related to sine and cosine graphs because of the identities from Unit Q, and because of tangents ratio. As we previously learned, Tan=sinx/cosx which means that an asymptote would appear when cosine is equal to 0. The ratio from the unit circle for tangent is y/x, which also applies if x equals 0 then it will be undefined and have asymptotes. Depending on the sign of each x and y value will determine the direction of the graph.
B) Cotangent
Cotangent is the reciprocal of tangent which makes it also related with sine and cosine except the ratio is x/y. In this case, when y is equal to 0 there will be asymptotes. The direction of the graph depends on the value of sine (x).
C) Secant
Secant is the reciprocal of cosine which makes if closely related to cosine. The ratio for secant is r/x. The sign of x is the determining factor for the asymptotes. We know the right sign for x when we do ASTC per the quadrants in the unit circle.
D)Cosecant
Cosecant is the reciprocal of sine which makes the ratio r/y. Since r is always equal to one, the determining factor for the asymptotes is the y value of the graph. The graphs never touch the asymptotes but they come very close just as in every other graph.
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