I am working on something not associated with homework and I need some help figuring out how to calculate the points of a graph. I'd like to have an exponential curve with 72 datapoints where every 8 points a new sinwave starts. The math is way over my head but I am sure my fellow math nerds know how to solve it quickly. The image below provides you a better idea of what I am thinking of. Don't take the image literally for anything. It is just an example.
Simply put, all you'd need to do is add the two different parts of it together. The first part would be your sine function, and the second part your exponential curve. For the sine curve to repeat every 8 points, all you'd need is x={0,1,2,3....}, y=x*sin(2*pi/8).
Thank you for your reply; however, I am unable to make your equation result in the desired effect. What it produces is a linear line with no cyclical pattern.
^I don't think that's quite it either. That's more or less a regular looking sine wave. Anyway if I'm understanding the question. I agree about the basic idea, that is exponential (say x^2) plus sine wave (sin (x)). That doesn't lead to much of a nice looking line though. Just messing around with the values on a graph, (x/5)^1.5+sin(2x) looks decent enough to me. It shouldn't be hard to get points from there. Sine has a period of 2pi, and since i'm using 2x inside of sin, that means the period is effectively just pi. So to get it to cycle every 8 data points, make x = 0, 1*pi/8, 2*pi/8... anyway solving all those to get the data points is an easy job for a spreadsheet so I come up with: Code: 0 0 0.3926990817 0.7291175302 0.7853981634 1.0622557996 1.1780972451 0.8214779881 1.5707963268 0.1760859923 1.9634954085 -0.4610191258 2.3561944902 -0.676509376 2.7488935719 -0.2994620043 3.1415926536 0.4980463969 3.5342917353 1.3013970052 3.926990817 1.6960409996 4.3196898987 1.5101221362 4.7123889804 0.9149696554 5.1050880621 0.3245847142 5.4977871438 0.1529935441 5.8904862255 0.5716021856 6.2831853072 1.4086879383 6.6758843889 2.2499017152 7.0685834706 2.6809065895 7.4612825523 2.5300167649 7.853981634 1.9687012432 8.2466807157 1.4110776136 8.6393797974 1.2712704116 9.0320788791 1.7207696326 9.4247779608 2.5879249918 9.8174770425 3.4584504107 10.2101761242 3.9180642099 10.6028752059 3.7951293683 10.9955742876 3.2611582147 11.3882733693 2.7303070404 11.780972451 2.6167351264 12.1736715327 3.0919638054 12.5663706144 3.984371175 12.9590696961 4.8796969634 13.3517687778 5.3636830392 13.7444678595 5.2647139396 14.1371669412 4.7543217918 14.5298660229 4.2466811203 14.9225651046 4.1559680438 15.3152641863 4.6537194821 15.7079632679 5.5683279968 16.1006623496 6.4855467673 16.4933614313 6.9911301974 16.886060513 6.9134745293 17.2787595947 6.4241228398 17.6714586764 5.9372599147 18.0641577581 5.8670715044 18.4568568398 6.3851035845 18.8495559215 7.3197572435 19.2422550032 8.2567937006 19.6349540849 8.7819749512 20.0276531666 8.7237044151 20.4203522483 8.2535319631 20.81305133 7.7856488204 21.2057504117 7.7342468472 21.5984494934 8.2708778224 21.9911485751 9.2239483526 22.3838476568 10.1792249093 22.7765467385 10.7224744918 23.1692458202 10.6821052918 23.5619449019 10.2296717345 23.9546439836 9.7793693959 24.3473430653 9.7453942958 24.740042147 10.2993021934 25.1327412287 11.2695035065 25.5254403104 12.2417683587 25.9181393921 12.8018672519 26.3108384738 12.7782117386 26.7035375555 12.3423594718 27.0962366372 11.9085091285 27.4889357189 11.8908597108 27.8816348006 12.4609698467
Thats it! I was able to configure the variables a little to work like I wanted. I ended with: Y=(X/16)^2+COS(7*X) Thank you.