BQ#4 Unit T: Concept 3 Tangent and Cotangent Graphs

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

The reason for this is that both tangent and cotangent have asymptotes in different places on their graph due to the fact that they have different ratio identities. Tangent has cosine in the bottom and cotangent has sin in the bottom. When you look at the pictures below, you can see the differnece between the two graphs, the asymptotes are in different places.

 y=tan(x)

http://www.regentsprep.org/Regents/math/algtrig/ATT7/othergraphs.htm

Ratio for Tangent is: sin/cosine

Asymptotes will happen when cosine equals to zero.

 y=cot(x)

http://www.regentsprep.org/Regents/math/algtrig/ATT7/othergraphs.htm

Ratio for cotangent is: cosine/sin
Asymptotes happen when sin equals to zero.

http://www.regentsprep.org/Regents/math/algtrig/ATT7/othergraphs.htm