A numerical method of harmonic analysis
639
Table 70.1
Ordin-
ates θ◦ V cosθ Vcosθ sinθ Vsinθ cos2θ Vcos2θ sin2θ Vsin2θ cos3θ Vcos3θ sin3θ Vsin3θ
y 1 30 62 0.866 53.69 0.5 31 0.5 31 0.866 53.69 0 0 1 62
y 2 60 35 0.5 17.5 0.866 30.31 −0.5 −17.5 0.866 30.31 − 1 − 35 0 0
y 3 90 − 38 0 0 1 − 38 − 1 38 0 0 0 0 − 1 38
y 4 120 − 64 −0.5 32 0.866 −55.42 −0.5 32 −0.866 55.42 1 − 64 0 0
y 5 150 − 63 −0.866 54.56 0.5 −31.5 0.5 −31.5 −0.866 54.56 0 0 1 − 63
y 6 180 − 52 − 1 52 0 0 1 − 52 0 0 − 1 52 0 0
y 7 210 − 28 −0.866 24.25 −0.5 14 0.5 − 14 0.866 −24.25 0 0 − 1 28
y 8 240 24 −0.5 − 12 −0.866 −20.78 −0.5 − 12 0.866 20.78 1 24 0 0
y 9 270 80 0 0 − 1 − 80 − 1 − 80 0 0 0 0 1 80
y 10 300 96 0.5 48 −0.866 −83.14 −0.5 − 48 −0.866 −83.14 − 1 − 96 0 0
y 11 330 90 0.866 77.94 −0.5 − 45 0.5 45 −0.866 −77.94 0 0 − 1 − 90
y 12 360 70 1 70 0 0 1 70 0 0 1 70 0 0
∑^12
k= 1
yk=( 212 )
∑^12
k= 1
ykcosθk
∑^12
k= 1
yksinθk
∑^12
k= 1
ykcos2θk
∑^12
k= 1
yksin2θk
∑^12
k= 1
ykcos3θk
∑^12
k= 1
yksin3θk
= 417. 94 =− 278. 53 =− 39 = 29. 43 =− 49 = 55