Question

How do you find the value of ${\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right)$ ?

Answer 1

In this question we are asked to find the value of ${\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right)$. This question can be solved by using the formula ${\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right) = y$.

Complete step by step answer:
We are asked to find the value of ${\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right)$
Say this function is equal to y.
$\Rightarrow y = {\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right)$
The best method to solve this question is by following the integral by numerical methods to get ${\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right)$
$\Rightarrow {\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right) = \int_0^{4/3} {\dfrac{1}{{1 + {x^2}}}dx}$
Which is approximately equal to 52.5 degrees.

Note: Trick to remember-
$\tan x = \dfrac{3}{4}$ here the numerator is equal to $3$ and angle is equal to ${37^ \circ }$
$\tan x = \dfrac{4}{3}$here the numerator is equal to $4$ and angle is equal to ${57^ \circ }$
This is only valid for above angle in terms of $\tan x$