BQ #4: Unit T Concept 3: Tanget and Cotangent Behavior

 

1. Why is a “normal” tangent graph uphill, but a “normal” Cotangent graph downhill? Use unit circle ratios to explain.

•  The reason for this behavior in a tangent graph and a cotangent graph is quite simple. It lies in the fact that tangent and cotangent have asymptotes in different spots on their graphs. This is  because tangent and cotangent graphs may have the same positive/negative pattern but since they have different ratio identities, they have different asymptotes. 
• If we remember how we get an asymptote, it is when we divide by zero and since tangent has the denominator cosine and cotangent has the denominator sine, the asymptotes will be in different spots. We can clearly see in this picture the difference between the asymptotes in both graphs. 

(http://www.analyzemath.com/trigonometry/graph_cotangent.gif)

(http://www.analyzemath.com/trigonometry/graph_tangent.gif)

 

 

 

 

References

http://www.analyzemath.com/trigonometry/graph_tangent.gif
http://www.analyzemath.com/trigonometry/graph_cotangent.gif