Unit T Big Question # 2

How do the graphs of sine and cosine relate to each of the others? 

a.) Tangent
b.)Cotangent
---The video will go over tangent and cotangent:



c.) Secant: Secant is the reciprocal of cosine. In order to graph the secant  graph we need to graph the cosine graph. Although cosine graphs do not have asymptotes secant graphs do so once we have draw the regular cosine graph we will then draw the asypmtotes for the secant graph. Secant is 1 / cos so the asymptote lies where cos is zero which is at pi/2 and 3 pi/2. So when we do draw the cosine graph with the secant asypmtotes the graph will look like this:

Now the only thing left to do is to draw the secant graph. Again secant is the reciprocal of cosine so its graph it going to be mirrored from it but as we do this we have to remember that the asymptotes are the barriers to our graph:(secant is represented by the green)

d.)Cosecant: For cosecant we follow the same concepts of that of cosine. First we draw the sine graph one a regular unit circle scale. Although sine does not have an asymptote, cosecant graphs do. Cosecant is 1/sin so whenever sine equals 0 there will be an asymptote since it will be undefined. This happens at 0, pi, and 2pi. So when we draw the sine graph with the cosecant asymptotes the graph will look like this:

Now the draw cosecant we see that there are two sets asymptotes so two graphs will be drawn. Again since  cosecant is the inverse of sine then the cosecant graph will be a reflection of the sine graph. Now when doing so we have to take two things into consideration:

                           *the sine graph was divided into two sections because of the asymptoes so that means there will be one cosecant graph in between each of the asymptotes for a total of two cosecant graphs. 

                         *Between 0 and pi cosecant is positive so the graph has to be reflected above the x-axis and cosecant is negative between pi and 2 pi so the graph needs to be reflected below the x-axis. 

The graph ends up looking like this:

                                                    

Citations for images:

http://www.biology.arizona.edu/biomath/tutorials/trigonometric/graphtrigfunctions.html
http://www.intmath.com/trigonometric-graphs/1-graphs-sine-cosine-amplitude.php