How to do trigeometry? what is the amplitude,period, horizontal shift,verical shift. How graph,find equation?

Question

How to look at the graph and know what is the amplitude, period, horizonal, and vertical shift. WITHOUT using a CALCULATOR. How to graph if you only the equation?

Answer 1

Nicole, the 10 Commandments took 256 words. How many do you think your query will take to answer? You gotta know the DEFINITIONS. The AMPLITUDE is how far displaced is the maximum or minimum "y" value from the average "y" value. In a simple trig function like the sine, the average "y" value is zero, and the maximum value will be 1 or -1. So the amplitude is 1 for such a function.

If you have heard about female "periods", the concept of a PERIOD should not be too hard to understand. The sine function is like a "wave", and in one period of x distance, will repeat exactly what it did in the previous period. In y= sin x, the period is from x=0 to x=2 pi . The reciprocal of period is called FREQUENCY, and the frequency will show up as the COEFFICIENT of x, if it is different from 1. If the frequency is 2, there will be two repetitions of the sine wave between 0 and 2 pi, and each will have a period of pi radians. So if you have data as a period, this will tell you the "space" in which the wave repeats. If you have data as frequency, it will tell you the number of TIMES it repeats between 0 and 2 pi radians. So you gotta watch out for this one.

Vertical shift should not be too hard to figure. Ordinarily, a trig function average "y" value is y=0. If it isn't, there is a vertical shift. For example, if we have y= 1+ sin x, it will look like y= sin x except that it one unit higher on the y axis than is y= sin x.

Horizontal shift should not be too hard to figure as long as you know the BEHAVIOR OF THE BASIC FUNCTION. In our example, if we note that the sin x=0 at pi/4 radians instead of at x=0, there is a horizontal shift of pi/4. In this case, the equation is y = sin (x - pi/4).

If you know the BEHAVIOR OF THE BASIC FUNCTION and the VERTICAL AND HORIZONTAL SHIFTS, you can easily graph the functions. What did you think people did before calculators?? Suppose you have
y = 4 + 7 sin (x+ pi/3). This has almost everything, so lets see how it breaks down. You have the sine function, but the arguement (this stuff) has a horizontal shift. It tells you that whatever sin looks at a given x+pi/3 radians, it will look like that at x radians. Our graph will be shifted pi/3 radians to the LEFT. The "7" is the AMPLITUDE, which tells you that you will have to go 7 units up and 7 units down from the average "y" value. The "4" is a vertical shift which tells us that the graph will run from y= +11 to y = -3 instead of from y = +7 to y = -7.

Now, if the function were y = 4 + 7 sin ( x/2 + pi/3 ), the x/2 will tell us that the function will be stretched out from 0 to 4 pi for one repitition as well as that the function will be shifted to the left. This is a FREQUENCY of 1/2 or a period of 2 pi

BTW: I hope you know the concept of radians. It can be hell if you don't.

Answer 2

Yeah, I'm not an Atheist, but I could probably take one of those shifts. You know, if you guys get tired of answering. You don't have to be an Atheist to understand that "Why wouldn't you believe in God, just in case He's real?" is a stupid question.

Answer 3

The amplitude is the biggest difference in the y direction. The period of a function is one complete wave.
http://campus.northpark.edu/math/PreCalculus/Transcendental/Trigonometric/Graphing/index.html
http://www.sparknotes.com/testprep/books/sat2/math2c/chapter9section5.rhtml