Graphing sine, cosine, tangent, cotangent, secant, and cosecant

 Date January 2006 Class Trig Teacher Terry Hagen Notes Graphing sine, cosine, tangent, cotangent, secant, and cosecant To begin the activity I had drawn on the board a graph in blue for the basis of the graph of sine and cosine. I had the students, groups of 4, find the sine in one and the cosine in the other. They found them in increments of 30 degrees. They then went to the board and plotted the results on the graph. They each had a different color for their graph so we could tell which one was sine and cosine by sight. The students had never seen a sine or cosine graph before so they had no idea what it would look like until all the plots were done. With both on the same graph we could then see the relationships they had. We then found out what they had in common and the different patterns they use. They discovered that they had functions that were cyclic. Then I had them do the tangent. They had never graphed an undefined trig function before so they were surprised at what it looked like. I then had them use a graphing calculator to graph the functions. We then found out what the co-functions like cosecant and cotangent looked like in comparison to sine and cosine. Going through this process helped my students visualize the different trig functions and how they were related. They now can draw the function without using the graphing calculator. I will use this again next year and try to find other ways to incorporate them into my other classes too.