"Is the arctan⁡ of a negative number always..." was answered by students like you

dublattm

Answered question

2022-01-25

Is the

\arctan

of a negative number always negative and

\arctan

of a positve number always positive?

SaphypycleDapc5

Beginner2022-01-26Added 11 answers

Hint:

\arctan (0) = 0,, \frac{d}{d x} \arctan (x) = \frac{1}{1 + x^{2}} > 0 .

Gordon Stephens

Beginner2022-01-27Added 10 answers

True. If

\tan^{- 1} x = θ \Rightarrow x = \tan θ

and

θ \in (- \frac{π}{2}, \frac{π}{2})

Thus if

x < 0

, then

θ < 0

, and the same is true for the positive case.

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