HARMONIC ANALYSIS 



397 



also 1-51 sin 6+1-21 cos - 1-93 sin (0 + 88-7) 

 0-59 sin 20 - 0-79 cos 20 = 0-97 sin (26 - 53-2) 

 0-20 sin 86 - 0-82 cos 86 = 0-38 sin (30 - 58) 



Then y = 3-29 + 1-93 sin (0 + 38-7) + 0-97 sin (20 - 53-2) 

 + 0-38 sin (30 - 58) 



i-zo 



I-9O 



FIG. 133. 



195. Example 2. The value of a periodic function of t is here 

 given for twelve equidistant values of / covering the whole period. 

 Express it in a Fourier's Series. Terms of the fourth and higher 

 orders are negligible. (B. of E., 1911.) 



2-340 

 0-825 



3-012 

 0-513 



3-685 

 0-875 



4-149 

 1-085 



3-685 

 1-189 



2-203 

 1-637 



Then B = (sum of the ordinates) 



25-198 

 12 



= 2-100 

 To get Aj and B x (Fig. 134). 



Then A, = ^ (2-499 sin 30 + 2-810 sin 60 + 8-064 + 2-496 sin 60 



D 



+ 0-566 sin 30} 



- ^ (8-064 + 8-065 sin 30 + 5-806 sin 60} 

 = 1-532 



