BQ #4 Unit T- Concept 3

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

From Mrs. Kirch's SSS packet

tangent: Quadrant 1 is postive, 2 is negative, 3 is postive, and 4 is negative. The ratio for tangent is Tan(x)= y/x. So as you can see when cosine equal zero that means that there is an asymptote. There is an asymptote because when it is zero, it is undefined which means there is an asymptote where ever x equals zero. Tangent has asymptotes at pi/2 and 3pi/2 because that is where x equals zero. So as you can see in the picture above pi/2 is before quadrant 2 which is negative, so the graph will start at the bottom and work its way up because the quadrant before 3pi/2 is postive.

cotangent: The quadrant have the same signs as tangent but the ratio for cotangent is cot(x)=x/y. So as you can see, now it is when sine equals zero where their is an asymptote. There is an asymptote at zero and pi for cotangent because that is where y equals zero. So as you can see in the picture above, the quadrant after 0 is postive and the quadrant before pi is negative. So the graph will start on the top and then go downhill.

So tangent goes uphill and cotangent goes downhill because of the location of their asymptotes.