logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
0 votes

Find the principal values of the following: \[ tan^{-1} (-1)\]

$\begin{array}{1 1} \frac{-\pi}{4} \\ \frac{\pi}{4} \\ \frac{-\pi}{2} \\ \frac{\pi}{2} \end{array} $

Can you answer this question?
 
 

2 Answers

0 votes
Ans : \( tan^{-1}tan \frac{-\pi}{4}=\frac{-\pi}{4} \)
answered Feb 22, 2013 by thanvigandhi_1
 
0 votes
Toolbox:
  • The range of the principal value of $\; tan^{-1}x$ is $\left [ -\frac{\pi}{2}, \frac{\pi}{2} \right ]$
Let $\;tan^{-1}-1= x \Rightarrow tan (x) = -1$
We know that the range of the principal value of $\; tan^{-1}x$ is $\left [ -\frac{\pi}{2}, \frac{\pi}{2} \right ]$
Therefore, $tan (x) = -1 = - tan \frac{\pi}{4} = tan \frac{-\pi}{4}$
$\Rightarrow x=\frac{-\pi}{4}$, where $x \;\epsilon\;$ $\left [ -\frac{\pi}{2}, \frac{\pi}{2} \right ]$
Hence the principal value of $x=\frac{-\pi}{4}$
answered Mar 2, 2013 by balaji.thirumalai
edited Apr 18 by meena.p
 
Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...