192 CHAPTER 5 • ELEMENTARY FUNCTI ONS
-------.-EXERCISES FOR SECTION 5.5
- Find all values of the following.
(a) arcsin ~·
(b) arccos ~-
(c) arcsin3.
(d) arccos3i.
(e) arctan 2i.
(f) arctan i.
(g) arcsinh i.
(h) arcsinh ~.
(i) arccosh i.0) arccosh!.
(k) arctanh i.
(I) arctanh i../3.2. Establish the following identities.(a) arccosz = - ilog [z + i (1 -z^2 )! J.
(b) f.arccosz= ~.
(1-»)>(c) arctanz = pog(~).(d) dd• arctan z = 1 ;, 2.
( e) arcsin z + arccos z = ~ + 2nir, where n is an integer.(f) f.arctanhz = 1 _\2.
(g) arcsinh z = log [ z + (z^2 + 1) ~].(h) .... 4,arcsinh z = ( ,;2+1^1 ) 11 ,.
(i) arccosh z = log [z + (z^2 - 1)!].(j) f. arccosh z = -:--1-:,-.
(·•-1)2