8-2 Graphing Trig Functions!

So, this week I am going to teach you how to graph a trig function.

Graphing trig functions have 8 steps but you don't always need to use all of them. These 8 steps are:

1. First you are going to identify if there is a negative and you are going to figure out which way the graph will start.
2. The next thing you need to do is find the period. A period is how long it takes for a curve to repeat itself. To find a period you use the formula 2Pi/B.
3. The next step is to find the amplitude. An amplitude is how high or low a wire is from the origin. To find an amplitude you just look for the number in front of sin, cos, etc.
4. Once you do all of those steps are going to list your 5 important points, which are always going to be 0, Pi/2, Pi, 3Pi/2, and 2Pi.
5. The next step is to divide your important points by B.
6. The next step you my not always use. The only time you would use this is if anything was added or subtracted in parenthesis in your problem. If that happens then you would do the opposite for all 5 of your important points.
7. Now you would sketch the graph.
8. We never actually got to this step yet and we never used it but I'm going to tell you it anyway. You would use this step is anything was added or subtracted outside of the parenthesis. If anything was then you would shift points up or down.

NOTE: Amplitude cannot be negative. A negative in front of sin or cos flips the curve.

Now I am going to do an example of these types of problems.

Example: 4 sin x

1. There are no negatives in this problems and the graph should look like this:
2. P=2Pi/1 P=2Pi
3. Amplitude=4
4. 0, Pi/2, Pi, 3Pi/2, 2Pi
5. You would divide them all by B which is 1. So they will all stay the same.
6. There are no numbers in parenthesis being subtracted or added.
7. The sketch of the graph should look like this:

8. You don't have anything to do for this step.

And that is how you graph trig functions!

--Halie! :)