graph cosecant by hand

In this math example, we sketch the graph of a cosecant csc function entirely by hand. We first identify the basic shape of our function by looking at the reciprocal relationship between cosecant and sine. Then we look at how each number will impact the graph as transformations. The multiple in front of the function changes the values on the y-axis (similar to amplitude for sine and cosine). Then we use the value that is added to the entire function to apply it as a vertical transformation. Again, this impacts the vertical values on the y-axis. Finally, we have a number multiplied directly to x on the inside of the function. We use this to calculate the period of our graph and get values to label our x-axis. After we have all of this information, we put it together to get a nice graph of our cosecant graph. After this is done, we find the domain and range of the function.