How do I create a matrix with a sine and cosine function?

Individual elements of B are referenced using B[i,j], where i is the row and j is the column. Define each element within B as B[i,j] = sin(i) cos(j) where both i and j go from 1 to 10 [Hint: B[1,1]=sin(1)*cos(1)]. It's size has to be 10x10.

I know that to define i and j I have to type in the code:

i=[1,2,3,4,5,6,7,8,9,10];
j=[1,2,3,4,5,6,7,8,9,10]

Also when I'm creating the function B I know that I have to put the code:

B=sin(i).*cos(j)

But how do I repeat to create the matrix 10x10?

Thank you so much! :)

Answer 1

[Stephen23]

Use basic matrix multiplication:

>> V = 1:10;
>> B = sin(V.')*cos(V)
B =
   0.454649  -0.350175  -0.833050  -0.550022   0.238693   0.807955   0.634387  -0.122434  -0.766690  -0.706054
   0.491295  -0.378401  -0.900198  -0.594356   0.257933   0.873080   0.685521  -0.132303  -0.828488  -0.762966
   0.076247  -0.058727  -0.139708  -0.092242   0.040030   0.135499   0.106391  -0.020533  -0.128579  -0.118410
  -0.408902   0.314941   0.749229   0.494679  -0.214676  -0.726659  -0.570555   0.110115   0.689546   0.635011
  -0.518109   0.399053   0.949328   0.626795  -0.272011  -0.920731  -0.722935   0.139524   0.873705   0.804606
  -0.150969   0.116278   0.276619   0.182638  -0.079260  -0.268286  -0.210652   0.040655   0.254584   0.234450
   0.354971  -0.273403  -0.650412  -0.429435   0.186362   0.630819   0.495304  -0.095592  -0.598600  -0.551259
   0.534553  -0.411718  -0.979457  -0.646688   0.280644   0.949952   0.745879  -0.143952  -0.901434  -0.830142
   0.222669  -0.171502  -0.407994  -0.269379   0.116902   0.395704   0.310697  -0.059963  -0.375494  -0.345797
  -0.293936   0.226393   0.538577   0.355596  -0.154318  -0.522353  -0.410139   0.079155   0.495674   0.456473

[newbie]

Thank you so much!

Answer 2

[Walter Roberson]

In R2016b, you can just do

i=[1,2,3,4,5,6,7,8,9,10];
j=[1,2,3,4,5,6,7,8,9,10];
B = sin(i) .* cos(j).';

In earlier releases, see bsxfun() or repmat() or meshgrid() or ndgrid()

[Shruba Gangopadhyay]

use i=[1:10] saves some typing time

[Stephen23]

@Shruba Gangopadhyay: the square brackets are not required:

i = 1:10;

is faster and simpler.