A six point summery is identifying 6 major facts about the graph of a trig function is as followed.
1. Amplitude
This is simply how high a graph will go. This is found out by looking at the coefficient in front of the trig function. In the graph of y=sin(x2), there appears none but that is because it is actually 1, and mathematicians don't write the number one out most times(if at all).
Thus, this graph will have an amplitude of 1, which means its greatest height is 1 and lowest height is −1.
2. Period
The parent sine graph, y=sin(x), has a period of 2π since it takes 2π revolutions to complete one cycle of the graph.
To figure out the new period, simply divide 2π by the coefficient attached to your x value. In this case, the new Period is 4π, since the coefficient is one half.
3. Translation of the Graph Up or Down
This is simply the question will my graph move up, down, or not at all. Again the parent sine function y=sin(x) doesn't have a translation, but if it were y=sin(x)+1 it would be moved one unit up. This graph doesn't have any, but this is part of the process
4. Translation of the Graph Left or Right
This graph doesn't have any but it is also important to note. Lets say our function we must graph is y=sin(x+π). The entire graph would be shifted to the left one π units. It shifts to the right because in order for the function to be 0, it needs to have an x value of −π.
5. Five Number Summery
A five number summery is simply 5 points on your graph used to map out what you will draw. I detailed it in the following paragraph.
A sine curve sin(x) starts at the origin (0,0), has a maximum of 1 at x=π2, a zero at x=π, a minimum of −1 at x=3π2, and a zero at 2π. What I just did right there is a five number summery, where I identify.
6. Consider range and domain
This is huge when dealing with other trig functions. In this case the domain is all real numbers and the range is −1 to 1, written mathematically [−1,1].
The graph of sin(x) looks like this
graph{sinx [-10, 10, -5, 5]}
The graph of sin(x2) looks like this
graph{sin(x/2) [-10, 10, -5, 5]}
