Question

can anyone help with Matlab?

Answer 1

What problem are you facing in Matlab?

Answer 2

i have to write a program for this problem...
determine the number of terms necessary to approximate cosx to 8 significant figures using the Maclaurin series approximation. use x=0.3pi
\[cosx=1-(x ^{2}/2)+(x ^{4}/4!)-(x ^{6}/6!)+(x ^{8}/8!)...\]

i don't know where to begin. I took Matlab 2 summers ago and the school and instructor was horrible and i'm not just saying this. the instructor stayed on the first 2 chapters (learning the basic functions) for half the semester and barely taught us how to write our own programs. i think she's fired.

Answer 3

Here is matlab that should work

% cos(x) = 1 - (x^2)/2! + (x^4)/4! -(x^6)/6!+(x^8)/8!...
% let y= x*x
% cos(x) = sum( (-y)^n/(2n)! )
format short
x= 0.3*pi;
y= x*x;
for N= 1:6
n= 0:N;
s1= [(-y).^n./factorial(2*n) ]
mac= sum(s1);
cx= cos(x);
str= sprintf('%d terms. series: %12.10f cos(x): %12.10f\n %12.10f',...
N, mac,cx, (cx-mac));
disp(str);
end;

Answer 4

differetiate cos(x) iteratively at x=0
y = cos (t)
loop
{
y = diff( y , t);
sub(y, 0)
}

find the coefficients ... use the usual method.

Answer 5

@phi thx, did you solve the problem to 10 sig figures?

Answer 6

It prints out more than 8. I'll leave it to you to count the digits

Answer 7

ok, how do i format the number of digits? so far i was able to find the commands "short", "long", but not exact number of digits i want

Answer 8

try running the program.
the sprintf statement formats using the C style formatting
%12.10f means use 12 places (includes decimal point), with 10 places to the right of the decimal

Answer 9

ok, i'll try thx

Answer 10

Although be careful, because I can't count! where it says it is using n terms, it is really using n+1 terms, counting the initial 1

Answer 11

i'm actually really confused and writing everything out on paper to see where everything fits. why is y=x*x, if s1 suppose to equal the explicit form of the mac series, why is it (-y)^n instead of (-1)^n and where's x^(2n)? i'm comparing to the explicit form:
\[cosx=\sum_{n=0}^{\infty} \frac{ (-1)^n }{ (2n)! } x ^{2n}\]

Answer 12

you do know \( x^{2n} = (x^2)^n \), right?
and \( (-1)^n \cdot (x^2)^n= (-x^2)^n \)

Answer 13

ok thx

Answer 14

It just makes the code a little bit simpler (or maybe just a little bit more indecipherable).

Answer 15

ok, and back to the number of decimal places...how would changing the %12.10f change anything since it's after %?

Answer 16

See above for the explanation. %12.0f would print out up to 11 digits plus the decimal point with 0 of the digits to the right of the point.

It is easier to play with it.

Answer 17

it worked. thx again for the help