(11.34) Ci.0„50 + 0,82e-<^^/s)^-^^ 



The function f(|j., 9) can then be given by 



(11-35) f(ui,e) =- [1 +(0,50 + 0„82e~^'^^^' ) cos 26 + c, cos 46] 



IT ^ 



for -it/2 < e < 17/2. 



Since the values of c, are greater than one for small |jl, f((i,6) becomes 

 negative for near jiTr/2, and this is not permissible. To avoid this, C2 

 must be chosen so as to make f(|j., 6) everywhere positive. 



Sine e 



(11.36) cos2e = 2(cos 6)^ - 1 

 and since 



(11.37) cos4e = 8(cos e)'^ - 8(cos 6)^ + 1 

 equation (1L35) can be rewritten as equation (11.38). 



(11.38) iKv-, 6) ^ [1 - 0.50 " 0.82e"^^^^/s^ ^^ + C2] 



+ [1,00 + 1.64 e"^^'^/g) /^ ' 8c2](cose)^+8c2(cose)^ 



In order to keep the term independent of 6 always positive, the small- 

 est possible value of c^ is given by 



(11.39) C2 = 0.32e-<^"/g^^/' 



The function.., f((Ji, 9) can then be written in two alternative forms as 

 equations (11,40) and (11 41), 



236 



