Question

Find the exact value.
Write your answer in radians in terms of pi

Answer 1

\[\tan^{-1} (-1)\]

Answer 2

hmm, got a unit circle?

Answer 3

yeah

Answer 4

what do I do next?

Answer 5

ok, recall that \(\bf tan(\theta) = \cfrac{sin(\theta)}{cos(\theta)} \)

so for the fraction to be equals to 1, both terms above and below will have to yield the same same/same = 1

for the fraction to be negative, one of them has to be negative
same/-same = -1
-same/same = -1

so check your Unit Circle where the cosine and sine are the same, and different signs

Answer 6

since \(\bf tan^{-1} (-1)\) just means

what is the angle(s) whose tangent is -1

Answer 7

ummm 3pi/4 and 7pi/4 ?

Answer 8

Find the angles where the absolute values of sin x and cos x are the same. Now find, of those, the places where they are opposite signs. Now find the place where they meet both of the previous specifications, and are in the domain of the inverse tangent. That is your answer.

Answer 9

on the range from 0 to 2pi, 1 revolution, yes

Answer 10

The range of tan inverse of x is usually -pi/2 to pi/2.

Answer 11

I think your answer to this problem is -pi/4.

Answer 12

oh i see i see. thanks!

Answer 13

or one can say, from \(\bf \cfrac{3\pi}{4} + \cfrac{\pi}{2}n\)
where n is an integer > 0

Answer 14

No sweat. Do math every day.

Answer 15

well, >=0

Answer 16

Usually, when we are dealing with a function, we want it to give a single output for every element of the domain. That is the reason the range is restricted to ( -pi/2,pi/2).