## elica85 3 years ago can anyone help with Matlab?

1. hali

What problem are you facing in Matlab?

2. elica85

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.

3. phi

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;

4. experimentX

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.

5. elica85

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

6. phi

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

7. elica85

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

8. phi

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

9. elica85

ok, i'll try thx

10. phi

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

11. elica85

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: $cosx=\sum_{n=0}^{\infty} \frac{ (-1)^n }{ (2n)! } x ^{2n}$

12. phi

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

13. elica85

ok thx

14. phi

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

15. elica85

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

16. phi

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.

17. elica85

it worked. thx again for the help