I know arctan (-1) = 3pi/4 but does it also equal 7pi/4?

1 Answer
Sep 11, 2015

Answer:

...or, alternatively "No"

Explanation:

In order to be treated as a function (which means it can not map into more than one value)
the range of #arctan# is restricted.

The most common version is that
#color(white)("XXX")-pi/2 < arctan(theta) <= pi/2#
although you will see
#color(white)("XXX")0 <= arctan < pi#

The second version is the one you refer to initially
#color(white)("XXX")#(otherwise #arctan(-1) = -pi/4#)
but for neither version is #(7pi)/4# within the defined range.