AcosΘ ーBsinΘ  =  C

e^(iΘ) = cosΘ ＋isinΘ
e^(-iΘ) = cosΘ ーisinΘ

 A(e^(iΘ)＋e^(-iΘ))ーB(e^(iΘ)ーe^(-iΘ))/ i =  ２C
(A＋ iB)e^(iΘ)＋(Aー iB)e^(-iΘ) =  ２C
e^(iΘ) = X
(Aー iB) X^２ー２CX＋(Aー iB) =  ０
X = ［ C ＋−√(C^２−(A＋ iB)(Aー iB))］/(Aー iB)
 = ［ C ＋−√(C^２−A^２−B^２)］/(Aー iB)
 = ［ C ＋−√(C^２−A^２−B^２)］(A＋ iB)/(A^２＋B^２)
C^２ = A^２＋B^２＋R^２とすると
R^２≧０の場合
= ［ C ＋−|R|］(A＋ iB)/(A^２＋B^２)
cosΘ
 = ［ C ＋−|R|］A/(A^２＋B^２)

R^２＜０の場合
= ［ C ＋−i|R|］(A＋ iB)/(A^２＋B^２)
cosΘ
 = ［ CA −＋|R|B］/(A^２＋B^２)

C^２≧A^２＋B^２の場合
Θ
 =arccos(［ C＋−√(C^２−A^２−B^２)］A/(A^２＋B^２))
C^２＜A^２＋B^２の場合
Θ
 =arccos(［ CA−＋B√(A^２＋B^２−C^２)］/(A^２＋B^２))