Big Question Blog Post Unit T Question 2

Question:
2. How do the graphs of sine and cosine relate to each of the others?
a. tangent?
b. cotangent?
c. secant?
d. cosecant?

Explanation: 
a. The sine and cosine graphs explained in the first concept relate to the tangent graphs by them dealing with writing the domain the same way and following almost the same process to finding the period shifts and the rest. The difference now is that we are dealing with figuring out the asymptotes in the graph due to the ratio of sin/cos where cosine for tangent at times will equal zero to give you an undefined answer which will lead you to having to draw asymptotes. 

b. For Cotangent graphs it is the same as tangent graphs except now the difference is that the ratio of a cotangent graph is different meaning the asymptotes will change. Now, the ratio is cos/sin where now sin becomes the one that is equal to zero at some point with the reference points meaning that asymptotes will have to be drawn and solved for.

c. The sine and cosine graphs are similar to the secant graphs in the sense that the secant graph follows the same process when you do cosine graphs except now you have to worry about asymptotes. Being that one of the values of the ratio of secant has a denominator of zero allows you to recognize that there will be use of an asymptote. Asymptotes are  use when you get an undefined answer and this is shown through secants ratio which is r/x where at one point x is equal to zero making the solution undefined because r always equals 1. So when drawing these asymptotes and labeling them on our graph we have to take a look at it and draw our parabolas that lie between these asymptotes. Also it can be explained as secant equalling 1/cos, where at one point cosine in that function will equal zero meaning that a asymptote will appear. 

d. As far as cosecant goes it also follows the same process as a sine graph yet now we are dealing with the ratio of r/y where y at one point is equal to zero. The denominator can never be zero but at one point with the given reference angle ordered pairs it is clear that the denominator (or x) will be zero which will give you an answer that is undefined. As stated before these undefined solutions allow you to plot the asymptotes and change the way the graphs are made because it now becomes a u shape (parabola). This one can also be explained as cosecant equalling the ratio of 1/sin. it is evident that sin will have to equal zero at one point which will make an asymptote appear.