Matlab help please For a square matrix A (i.e dimensions nxn), the matrices of s
ID: 3403480 • Letter: M
Question
Matlab help please
For a square matrix A (i.e dimensions nxn), the matrices of sin(A) and cos(A) can be obtained as follows (-1) cos( A I (2k)! A3 A5 A7 2k+1 (-1) sin (A) A Where I is the nxn identity matrix (diagonals terms are all equal to 1 and off-diagonal terms are all equal to zero) 2k+1 The partial sums CN (A 30-1) and S (A (-1) can thus be used to 2k +1)! k-0 approximate the matrices sin(A) and cos(A) respectively 1. Write a Matlab function matcosin' having for input a square matrix A and for output the matrices cos(A) and sin(A). Use a control flow block (for, if or while) to compute the partial sums CN (A) and Sw (A) for a sequence of N 0,1,2 etc. Stop the loop once the following criterion is fulfilled max (CN I (A)-CN (A), SNI (A)-SN s0.01 (A)) N.B: cos(A) is NOT the matrix obtained by computing the cosine of the individual elements of the matrix A. 2. Let a, a 22 Where a, I, a12, ah, and ana are the last four digits of your student ID a. Use the function matcosin to compute cos(A) and sin(A) b. Compute (cos(A) (sin(A))?Explanation / Answer
The function is
function [cos_A,sin_A]=matcosin(A)
%%
I=eye(size(A)); % Identity Matrix
cos_N_plus_1=0;
sin_N_plus_1=0;
cos_N=0;
sin_N=0;
tolerance=0.01;
for k=0:10000
cos_N_plus_1=cos_N+(((-1)^k)*(A^(2*k))*(1/factorial(2*k)));
error_cos=abs(cos_N_plus_1-cos_N);
sin_N_plus_1=sin_N+(((-1)^k)*(A^(2*k+1))*(1/factorial(2*k+1)));
error_sin=abs(sin_N_plus_1-sin_N);
max_error=max(error_cos,error_sin);
if max_error<=tolerance
break
end
cos_N=cos_N_plus_1;
sin_N=sin_N_plus_1;
end
fprintf 'cos(A) is %f and sin(A) is %f ',cos_N, sin_N
cos_A=cos_N;
sin_A=sin_N;
#####################################################################################
save the above function as matcosin.m file.
The seocnd part of the question can be done by creating your own matrix
Here Assuming the last 4 digits are 1021
we have :
clear all
clc
%%
A=[1,2;0,1];
[C,S]=matcosin(A)
sum=(C^2+S^2)