BQ#4 - Unit T Concept 3

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 A "normal" tangent graph goes uphill, whereas a "normal" cotangent graph goes downhill. This is due to the ASTC pattern for tangent and cotangent: positive (I), negative (II), positive (III), and negative (IV).  In the last unit, we learned about the ratio identities for tangent and cotangent: tanθ = sinθ/cosθ; cotθ = cosθ/sinθ.
Since asymptotes only exist when there is an undefined, in tangent, cos must equal 0. Thus, cos=0 at 90 degrees and 270 degrees, which is (+)(-)pi/2. Thus, the formula to find the asymptotes for tangent would be b(x-h)= (+)(-)pi/2.
In cotangent, sin must equal 0.  Moreover, sin=0 at 0 degrees and 180 degrees, which is 0 or pi. Therefore, the equation to find the asymptotes for cotangent would be b(x-h)=0 or b(x-h)=pi.
Therefore, he only way for the graph to drawn according to the pattern and without crossing the asymptotes would be in an uphill graph for tangent, and downhill graph for cotangent.