THE SINE AND COSINE SERIES 



55 



The method of finding the relation which gives the approximate 

 length of a circular arc is a good application of the use of the 

 sine series. 



Let ABC (Fig. 17) be the circular arc and AB the chord of the 

 whole arc, BC the chord of the semi-arc. 



FIG. 17. 



Let arc ABC = I, chord AB = c, chord BC = h, angle AOB = - 

 radians. 



Then -r-pr = sin 

 AO 2r 



c . I 

 or = sin 

 2r 2r 



CE I 



M * co = sm 47 



h . i 



= sin 

 Z 3 



c .11 



Then 2~r = " 27 ~ 2r 8^^ 32Jp . . . 



!L-- s i n J- -L f l \ 



2r 4r 4r 64(3?^ 1024157* . . . 



73 75 



v 



41- 



4|3r 2 16J5? . . . 



> 



64I5/ 4 . . . 

 3/5 



By subtraction 8h c = 31 > i, . 



64|5r* . . . 



8/i-c 

 and ^ = 



