Explain why tan pi=0 does not imply that arctan0=pi?

1 Answer
Sep 10, 2015

Answer:

#pi# is not in the interval used for #arctan#

Explanation:

We want #arctan# to be a function. We want it to give one, never two, values for a single input.

By definition:

#y = arctan x# if and only if (#tan y = x# and #-pi/2 < y < pi/2#)

Since #pi# is not in #(-pi/2, pi/2)# there is no #x# for which #arctanx = pi#

(The situation is similar to: Explain why #(-3)^2 = 9# does not imply that #sqrt9 = -3#. It (#-3#) is the wrong kind of number to be a principal square root.)