I have to write my own cosine function.

I have to write my own cosine function using taylor series with inputs x and N for the degree. So i have figured out how to do the for loops for the n but the taylor series for cosine is

1-(x.^2/2!)+(x.^4/4!)-(x.^6/6!)...etc

so, my question is what can i use in my function to alternate between subtracting and adding after every loop. Sorry if i make no sense i am failry new to programming. thank you!!!

[James Tursa]

You can use (-1)^some_power to get the alternating signs, but perhaps a more simple approach is to have a variable that simply flips signs each iteration. E.g.,

the_sign = 1;
for k=1:N
    % other code here
    your_term = the_sign * other_stuff;
    % other code here
    the_sign = -the_sign;  % <-- flips signs each iteration
end

Answer 1

[KSSV]

Note that you can represent the above series as follows:

With the above it makes easy to write your function.

As this is an home work problem..I am giving you a hint..not the complete code.

x = pi/4 ;
n = 100;
c = 0 ; 
for i = 0:n
    % Write your formula here
end

[Torsten]

And work with y = mod(x,2*pi) instead of x.

[James Tursa]

Not really in scope for this thread, but if you want to effectively use the same mod 2pi that MATLAB uses (which is some type of sophisiticated extended precision algorithm that is part of the trig library code):

xmod2pi = atan2(sin(x),cos(x));

To see the difference for large values:

>> x = 1e16
x =
     1.000000000000000e+16
>> xmod2pi = atan2(sin(x),cos(x))
xmod2pi =
   2.247425249162367
>> mod(x,2*pi)
ans =
   2.637242432414304
>> sin(x)
ans =
   0.779688006606979
>> sin(xmod2pi)
ans =
   0.779688006606979
>> sin(mod(x,2*pi))
ans =
   0.483238668387966