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 New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Reference Information Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55) Purchase the electronic edition of this book in Adobe PDF format! FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | MEDIUM | LARGE Below is the OCR-scanned text from this page: ELEMENTARY TRANSCENDENTAL FUNCTIONS 79 - I 0 + I 4.3.1448 Formul& for Solution of Plane Triangles 0 R In a triangle with angles A, B and C and sides opposite a, b and c respectively, a b c sin A sin B sin C .--=-=- c2+ b2-a2 2bc cos A= a= b cos C+c cos B a + b tan +(A+B) a-b-tan #(A-B) -- -[s(8-a) (8- b ) (8-c)]' bc sin A area=-- 2 S= 4 (a + b +c) 4.3.149 Formulas for Solution of Spherical Triangles If A, B and C are the three angles and a, b and c the opposite sides, sin,A sin B sin C sin a sin b sin c -- --=- cos a=cos b ws c+sin b sin c ws A - ms b cos (eke) cos e - where tan B=tan b cos A cos A= -cos €3 cos C+sin B sin C cos a 4.4. Inverse Circular Functions Definitions 4.4.1 arcsin z=J' (2 = x+ iy) (1-t2)+ 4.4.2 arcsin z arccos z=J -=-- at P (1-P)t 2 4.4.3 arctan z=Jz dt 0 l + t 2 8 The path of integration must not cross the real axis in the case of 4.4.1 and 4.4.2 and the imaginary axis in the case of 4.4.3 except possibly inside the unit circle. Each function is single- valued and regular in the z-plane cut along the real axis from - 00 to - 1 and +1 to + OD in the case of 4.4.1 and 4.4.2 and along the imaginary axis from i to i 00 and --i to --i 00 in the case of 4.4.3. Inverse circular functions are also written arcsin z=sin-' z, arccos z=cos-I z, arctan z =tan" z, . . . . When -1 5x5 1, arcsin z and arccos z are real and 4.4.4 4.4.5 4.4.6 arccsc z=arcsin l / z 4.4.7 arcsec z=arccos l / z 4.4.8 arccot z=arctan l / z 4.4.9 arcsec z+arccsc Z = ~ T - 4..