In a similar manner, one can define the 'arccosine' and 'arctangent' functions by 'restricting the domains'. The
following table summarizes the domains and ranges of these inverse functions.
Function
Domain Range
Function
f(x) = sin¯¹(x)| (-1,1)|(−½, 3) || f(x) = sec¯¹(x)
f(x) = cos ¹(x) [−1,1]
f(x) = tan-¹(x)
[0, π]
Domain Range
R (-)|| f(x) = cot-¹(x)
x2! [-7,7-
XZ1
OY
f(x) = csc¯¹(x)
85-1
xs-1 but fuxito
Exercise 4.
(a) Sketch the graph y = tan-¹(x)
(b) From (a), write down lim tan-¹(r) and lim tan-¹(x).
x48
8118
(c) Look up the relevant section in the textbook (Stewart), write down the domains and ranges of the 'inverse
reciprocal trigonometric functions' on the right hand side of the above table.
