I'm a math student currently facing the following dilemma: finding the values for a function. The problem seemed easy but I don't even know how to call it properly, but I believe it can be written as a sum of sine and cosine functions.
For the problem: Imagine you have a useless lock with 1 digit, it has 5 numbers written on it: 5,4,3,2 and 1; The function begins without you rotating the digit and with the number 5 (point: 5,0), after rotating the lock once the number in display is 4 (point: 4,1), repeat the process 3 (point: 3,2), 2 (point: 2,3), 1 (point: 1,4) until it goes back to 5 (point: 5,6).
How can I write this as a function?
A model of the form
$ a \cos \left(b+\frac{2 \pi t}{5}\right)+c \cos \left(d+\frac{4 \pi t}{5}\right)+e \cos \left(f+\frac{6 \pi t}{5}\right)+g \cos \left(h+\frac{8 \pi t}{5}\right)+3 $
where a,b,c,d,e,f,g,h are parameters
will fit to the solution:
$ 0.412713 \cos \left(\frac{2 \pi t}{5}+0.227908\right)+0.789855 \cos \left(\frac{4 \pi t}{5}+0.514379\right)+0.778897 \cos \left(\frac{6 \pi t}{5}+1.15817\right)+1.58662 \cos \left(\frac{8 \pi t}{5}+1.18438\right)+3 $
which repeats as desired.