Table mix with If function

Question

Anyone could explain to me which problem is? after running the function "Table" combining with "If" as below, but the result is not a value instead.

 k:=8; n:=k+1; Alpha:=Pi/6; r:=3;
 In[5]:= Subscript[y, n][i_] := r cos[i \[Alpha]]
In[6]:= Subscript[y, n] = 
 Table[if [i == 1, Subscript[y, n][0], Subscript[y, n][i]], {i, 1, n}]
Out[6]= {if[True, 3 cos[0], 3 cos[[Pi]/6]], 
 if[False, 3 cos[0], 3 cos[[Pi]/3]], 
 if[False, 3 cos[0], 3 cos[[Pi]/2]], 
 if[False, 3 cos[0], 3 cos[(2 [Pi])/3]], 
 if[False, 3 cos[0], 3 cos[(5 [Pi])/6]], 
 if[False, 3 cos[0], 3 cos[[Pi]]], 
 if[False, 3 cos[0], 3 cos[(7 [Pi])/6]], 
 if[False, 3 cos[0], 3 cos[(4 [Pi])/3]], 
 if[False, 3 cos[0], 3 cos[(3 [Pi])/2]]}

Try If[] instead of if [] all MM functions start with Capitals — Lou, Jun 19 '22 at 12:26
Note also that the cosine function is Cos and the imaginary unit is I. When you define constants, you don't need to use SetDelayed (:=); use Set (=) instead (see this FAQ). — MarcoB, Jun 19 '22 at 12:39
Welcome to the Mathematica Stack Exchange. The introductory book written by the inventor is a good learning resource. There is a fast intro for math students as well as a fast intro for programmers to choose from. — Syed, Jun 19 '22 at 13:47

score 1 · Accepted Answer · answered Jun 19 '22 at 17:38

I assume you want something like the following:

Subscript[y, n][i_] := r Cos[i α] /. {r -> 3, α -> π/6}
Table[If[i == 1, Subscript[y, n][0], Subscript[y, n][i]], {i, 1, 9}]
(*{3, 3/2, 0, -(3/2), -((3 Sqrt[3])/2), -3, -((3 Sqrt[3])/2), -(3/2), 0}*)

Or in the same way:

Module[{s}, With[{k = 8}, s = k + 1; Table[If[i == 1, Subscript[y, n][0], Subscript[y, n][i]], {i, 1, s}]]]
(*{3, 3/2, 0, -(3/2), -((3 Sqrt[3])/2), -3, -((3 Sqrt[3])/2), -(3/2), 0}*)

Table mix with If function

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