Expression 5: alpha equals left bracket, 0 , StartFraction, pi Over "N" , EndFraction , ... , StartFraction, left parenthesis, "N" minus 1 , right parenthesis pi Over "N" , EndFraction , right bracketα=0,πN,...,N−1πN
equals=
00
1.0 4 7 1 9 7 5 5 1 21.0471975512
2.0 9 4 3 9 5 1 0 2 3 92.09439510239
5
Expression 6: cosine left parenthesis, alpha , right parenthesis "x" minus sine left parenthesis, alpha , right parenthesis "y" equals "b" sine left parenthesis, 2 pi left parenthesis, sin left parenthesis, alpha , right parenthesis "x" plus cos left parenthesis, alpha , right parenthesis "y" , right parenthesis , right parenthesis left brace, negative 1 less than or equal to sin left parenthesis, alpha , right parenthesis "x" plus cos left parenthesis, alpha , right parenthesis "y" less than or equal to 1 , right bracecosαx−sinαy=bsin2πsinαx+cosαy−1≤sinαx+cosαy≤1