Precal Blog

So today in class we were given a worksheet to do.  The first three problems on the worksheet dealt with csc and sec graphing and the last problem dealt with tan which we will be learning tommorow.  One of the three problems we were supposed to do in class today was graph y=3+csc6( theta-30). To do this we first need to find the asymptotes and the high and low points of the sine graph since it is csc.  We know the vertical midline of the sine graph is 3 since it is 3+csc6( theta-30). Then the amplitude is one and since the midline is three the graph’s vertical high point would be 4 and its vertical low point would be 2.  Then we need to determine the period by dividing 360 by 6 which gives us a period of 60.  Since the equation has theta minus 30 in it the graph starts at 30 on the x axis.   Then we can plot the sine graph (or you can just do this next step in your head thus taking off the training wheels) and where ever the graph crosses the midline which in this case is 3 we illustrate a veritcal asymptote. Knowing this we can now plot the sec graph which looks like this(without the sine graph and the asymptotes):

After we completed the worksheet Mr. Bieniek threw an unexpected curve ball at us as we were asked to find the equation from the graph this time. He gave us  this graph (link to graph click here and then put in pg 110 for the page on the lower left corner and it is #37.)  For this graph the first thing i did was find out whether it was sec or csc.  To do this i looked at where the high point would have been if we had plotted sine or cosine and realized it was not the starting point of the period but instead it is at 3 on the x axis which is a quarter of the way through the period which is 12.  This meant it had to be csc (the reciprocal of sine)  because cosine graphs always start at their high point.  Then i noticed the amplitude was 1 and since the high and low points were at 1 and -1 the midline was at 0.  Since i figured out that the period was 12 i divided 360 by 12 and got 30.  With all this imformation i got the equation y=0+1csc(30theta).

The next scribe will be AJ.