Unit T Big Question#3

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

What is the concept about?

This concept is going to explain how tangent goes uphill and cotangent goes downhill. It will clarify why these two graphs have the different motion yet having the same pattern.

What the viewer needs to pay attention to in order to understand concept?

The viewer needs to pay attention to where the asymptotes are drawn for cotangent and tangent. This determines the way the graph will be shaped. They may have the same pattern, but the graphs are shifted differently when drawing them. We also need to remember the positive and negative pattern because we are going to use it.

Explanation:

There is a difference between the shapes of the graph because of  where the asymptotes are placed for tangent and cotangent. 

Tangent:

The tangent has the ratio identities of sin/cos. Since the asymptote is placed at pi/2 and 3pi/2 the graph is drawn going upward. The pattern is positive and negative, positive and negative. The negative is going upward to the next period which is positive, then the next period starts negative going up to positive. This gives it the uphill motion.

Cotangent:

The cotangent has the ratio identities of cos/sin. This means the asymptote are located in the 0 and pi. The pattern is positive and negative, positive and negative. This period starts at the positive and then goes down to the negative period. Then again it starts at the positive and goes down to the negative period. This gives it the downhill motion.