The "normal" tangent graph is uphill because of its asymptotes, which is located at pi/2 and 3pi/2 and so forth. The quadrants is positive, negative, positive, and negative. Tangent is uphill based on its asymptotes. Meanwhile, cotangent is downhill because its asymptotes is located at 0 and pi and so forth. In a way, it's asymptotes is "shifted" away from the "normal" tangent graph's asymptotes. Although the quadrants still apply the same for cotangent, it is a downhill because of where the asymptotes is located. Remember, tangent and cotangent have different asymptotes because of its ratio and the denominator in the ratio (sine or cosine will equal to 0).
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