Question

tan^-1(-1) = ?

Answer 1

7πover4

Answer 2

careful here

Answer 3

my trusty scientific calculator said -45 :DDD

Answer 4

range of arctangent is
\[[-\frac{\pi}{2},\frac{\pi}{2}]\]

Answer 5

so it should be
\[-\frac{\pi}{4}\]

Answer 6

apart from the angle in quadrant IV, you should also consider the tangent of an angle in quadrant II will also give -negative value. therefore the angles are -π/4 or 3π/4

Answer 7

nope

Answer 8

why?

Answer 9

tangent is periodic with period
\[\pi\] so there are an infinite number of numbers whose tangent is -1

Answer 10

hmm got it, thanks

Answer 11

\[\tan^{-1}(-1)\] does not mean SOME NUMBER whose tangent is -1 , it means the number in the itnerval
\[[-\frac{\pi}{2},\frac{\pi}{2}]\] whose tangent is -1, and there is only one such number because on that interval tangents is one to one and so the inverse is a function (well defined)

Answer 12

i am typong not so good the mroning

Answer 13

it's fine as long as we understand it.