6-3 Trigonometric Graphing Day 1 What do the graphs look like?

Sin x, Cos x, Get your chart out; I am going to use a graphing website to plot the points from your chart onto a set of axes. You will do a quick sketch in your notes. Graph y = cos x Graph y = sin x

Lets see if we can find some trends Lets look at the following graphs: What does this all mean?

Trends Remember back when we graphed step functions and looked at trends? f(x) f(x)+c f(x+c) f(cx) c(f(x)) Shift up/down Shift left/right changed step length Changed space between step

Basic Truths The period (that is, cycle length) of both y = sin x and y = cos x is 2π. The amplitude of both functions is 1. For a standard, we start both of these functions at x = 0 and finish at x = 2π.

So what trends do we observe? Add outside? Move graph  Add inside? Moves graph  Multiply outside? Changes Amplitude Multiply inside? Changes Period 

Do I have to memorize these? Well, to a degree you should know what to expect. Some teachers want you to look at the graph, determine where it will start and end, determine what the amplitude is, then just graph. I will teach you a mathematical method that you can memorize.

My Method Determine New Start: Set Argument = 0 Determine New End: (or New Start + Period) 3. Find 3 midpoints 4. Plot these 5 points

We will practice both methods; we’ll use the trends to predict what we think will happen, then use the mechanics to prove it. When it comes to a test, do whatever is easier for you to do.

Examples Graph the following completely 1. 2.