Higher Engineering Mathematics, Sixth Edition

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