A. Tangent
-Tangent is related to sine and cosine in the ratios. Tan=sin/cos, tangent is also y/x. Tangent will have asymptotes when x=0. The asymptotes depend or are related to sine and cosine. Depending what cosine is then the graph will have asymptotes. If tangent is undefined then asymptotes exist. If cosine is positive tangent will also be positive and if cosine is negative tangent will be negative and therefore below the x-axis.
B. Cotangent
-The ratio for cotangent is x/y or cosine/sine. The asymptotes for cotangent are different because sine now has to equal zero. Depending if sine is positive or negative the graph will be also positive or negative. The asymptotes are drawn depending on what sine is. The graph depends or what sine is.
C.Secant
-Cosine is positive in the first quadrant so secant is also positive. Secant equals one in this case. The ratio for secant is r/x. Secant will have asymptotes whenever cosine equals zero. The graph for secant will always be drawn at the top of every mountain and at the bottom of every valley of the cosine graph. The graph exist where the asymptotes are and they depend on cosine.
D.Cosecant
-The asymptotes will exist whenever sin(x)=0. Every cosecant graph has to touche the top and bottom of the sine graph. If sine is positive so is cosecant and if sine is negative so is cosecant. The graph is drawn where ever the asymptotes exist which are based on sine. The graph depends on what sine is.
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