Browse Questions

# True or False: The minimum value of n for which $\tan^{-1}\Large {\frac{n}{\pi}}\;>\Large {\frac{\pi}{4}},\normalsize\;n\in N,$ is valid is 5

$\begin{array}{1 1} \text{False, Minimum Value is 4} \\ \text{Yes Minimum Value if 5} \\ \text{False, Minimum Value is 3} \\ \text{Cannot be Determined }\end{array}$

Toolbox:
• $tan\large\frac{\pi}{4}=1$
• if x>$\large\frac{\pi}{4}$, then tanx >1
• The value of $\pi$ is 3.14 approximately.
Ans - False
we know if x>$\large\frac{\pi}{4}$, then tanx >1 and
$given:tan^{-1}\large\frac{n}{\pi}>\frac{\pi}{4}$

$\Rightarrow\:tan(tan^{-1}\large\frac{n}{\pi})>tan\large\frac{\pi}{4}$
$\Rightarrow\:tan(tan^{-1}\large\frac{n}{\pi})>1$
$\Rightarrow\: \large\frac{n}{\pi}>1 \Rightarrow n > \pi$
$\Rightarrow\:n>3.14$
$\Rightarrow\:$ minimum integer value of n =4

edited Mar 19, 2013