evaluating cos(x)

hamlet

need to evaluate it to whatever order term i want. I also need to display the relative error each time. My only problem is getting the sign to switch every other term. heres what I have:

[php]
function y=democos(x)
yexact=cos(x)
nmax=input('Enter highest order to which you want to evaluate:')
y=1
for i=1:nmax
y=y+(-1)(x^(i*2))/factorial(i*2)
error=((yexact-y)/yexact)*100
[/php]

hamlet

hamlet wrote:

need to evaluate it to whatever order term i want. I also need to display the relative error each time. My only problem is getting the sign to switch every other term. heres what I have:

[php]
function y=democos(x)
yexact=cos(x)
nmax=input('Enter highest order to which you want to evaluate:')
y=1
for i=1:nmax
y=y+(-1)(x^(i*2))/factorial(i*2)
error=((yexact-y)/yexact)*100
[/php]

updated code:

function y=democos(x)
yexact=cos(x)
nmax=input('Enter highest order to which you want to evaluate:')
y=1
for i=1:nmax
y=y+(-1)*(x^(i*2))/factorial(i*2);
error=((yexact-y)/yexact)*100;
disp([i,y,yexact,error])
end

I know the problem is somewhere between the = sign and first * in that 7th line. Obviously its just subtracting each term over and over instead of alternating +/-.

Thanks for any help.

shwaip

the easiest way to make the sign alternate is to replace -1 with -1^i.

When i is even, -1^i = 1. When i is odd, -1^i = 1.

You may need to add or subtract 1 from i to make sure it is even in the correct indicies.

hamlet

shwaip wrote:

the easiest way to make the sign alternate is to replace -1 with -1^i.

When i is even, -1^i = 1. When i is odd, -1^i = 1.

You may need to add or subtract 1 from i to make sure it is even in the correct indicies.

Thanks.. don't know why I didn't think of that. What do you mean in the correct indicies? There is something still wrong I can't figure it out.. my answers aren't converging towards the true value..

function y=democos(x)
yexact=cos(x)
nmax=input('Enter highest order to which you want to evaluate:')
y=1
for i=1:nmax
    y=y+(-1^i)*((x^(i*2))/factorial(i*2));
    error=((yexact-y)/yexact)*100;
    disp([i,y,yexact,error])
end

I am running it at cos(1.5) to 8 degrees.
It's giving me this:

y =

     1

    1.0000   -0.1250    0.0707  276.7104

    2.0000   -0.3359    0.0707  574.9092

    3.0000   -0.3518    0.0707  597.2741

    4.0000   -0.3524    0.0707  598.1727

    5.0000   -0.3524    0.0707  598.1952

    6.0000   -0.3524    0.0707  598.1956

    7.0000   -0.3524    0.0707  598.1956

    8.0000   -0.3524    0.0707  598.1956


ans =

   -0.3524

It is closer to yexact at the beginning? What the fuzzy no nosed chimp?

shwaip

you need parentheses around the -1

it should be (-1)^i instead of -1^i

hamlet

shwaip wrote:

you need parentheses around the -1

it should be (-1)^i instead of -1^i

gives me the same answers?

hamlet

nope never mind got it! Thanks a lot, appreciated.