BQ #4 Unit T Concept 3:

• Why is a “normal” tangent graph uphill, but a “normal” cotangent graph downhill? Use unit circle ratios to explain.
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     A "normal" tangent graph is uphill while a normal cotangent graph is downhill, not because it is the inverse of the other, but because of the positive/negative sign that corresponds to tangent in each quadrant. For example, tangent (and cotangent) are positive in the first and third quadrants, and negative in the second and fourth quadrants. They are arranged this way because of the unit circle ratios for these trig functions tan=y/x and cot=x/y. So for tangent, the graph will go--in one period--from negative (below the x-axis) to positive (above the x-axis). And for cotangent, the inverse of that rule applies.


Tangent

 Cotangent