Individual Periodic Functions Project

[inception]

I have the following homework assignment (senior in high school): there are two periodic functions to investigate of the form y=f(x)=a*sin(bx) c*cos(dx). You will find and organize values of each function into a table and plot the points in a graph. I have values for x, but need to organize values into a table then plot points in a graph and am lost at this point with how to proceed.

 

[tkhunny]

Have you tried substitution? It helps if you stick to standard, or well-known values.

 

[inception]

I have values for a, b,c, and d (1,2,3,3), giving me 1*sin(2x)+3*cos(3x). I have also calculated the values for x in the following table. My problem is solving for F(x) so that I can graph it. I'm unsure what to do at this point. Any help or suggestions would be appreciated.
x
-12.57
-11.00
-9.42
-7.85
-6.28
-5.50
-4.71
-3.93
-3.14
-2.62
-2.36
-2.09
-1.57
-1.05
-0.79
-0.52
0.00
0.52
0.79
1.05
1.57
2.09
2.36
2.62
3.14
3.93
4.71
5.50
6.28
7.85
9.42
11.00
12.57

 

[mmm4444bot]

My problem is solving for F(x) so that I can graph it.

I think that you mean "evaluating f(x)" instead of "solving for F(x)" because there is nothing to solve, when forming a table of (x,y) values to plot.

Your original post talks about two periodic functions; it now seems that there is only one function, and that you forgot to type the plus sign, in your original post.

Also, the names f and F are not the same, so please pick one and stick to it.

f(x) = sin(2x) + 3 cos(3x)

Your first x-value listed is -4 Pi (rounded to two places).

To "evaluate" f(x) when x = -4 Pi means to find the number which is represented by the symbol f(-4 Pi).

Finding this value is as simple as substituting the number -4 Pi for the variable x in your function definition, followed by using a scientific calculator to do the arithmetic with the sine and cosine values. If you're using a graphing calculator, you should be able to enter the following exactly as shown.

sin(2*(-12.57))+3*cos(3*(-12.57))

The result displayed should look something like 2.999999989 or 3.000000011.

This means that the value of f(x) is 3 when x is -4 Pi. In other words, the point (-12.57, 3) is on the graph of function f.

Most graphing calculators will generate such a table of (x,y) values for you automatically. You can specify the restricted domain from -4 Pi through 4 Pi. You can even specify the distance between x-values in the table (every Pi/2, for example).

Actually, the machine will draw the graph, too!

Is this exercise strictly an exercise in graphing?

 

[inception]

The first part is to graph...then I have to describe such properties as domain, range, zeros, period, and amplitude. Thank you sooo much for your help!!

 

[tkhunny]

You will also want to make sure you are in RADIAN mode and not DEGREE mode.

 

[inception]

You must have been reading my mind 'cause I kept getting 1.94 in Degree mode and was about to email you again. Once again...thanks! This was driving me crazy.

 

[Denis]

You must have been reading my mind 'cause I kept getting 1.94 in Degree mode and was about to email you again. Once again...thanks! This was driving me crazy.

Well, look on positive side: it'll never happen again, right ? :idea: