# How do you calculate tan^-1 (12.4304)?

$\setminus {\tan}^{- 1} \left(12.4304\right) = {85.4}^{\setminus} \circ$

#### Explanation:

One can compute $\setminus {\tan}^{- 1} \left(12.4304\right)$ using calculator which gives

$\setminus {\tan}^{- 1} \left(12.4304\right) = {85.4}^{\setminus} \circ$

Jul 16, 2018

Approximately $85.40$ degrees rounded to 2 decimal places.

#### Explanation:

$\textcolor{b l u e}{\text{The teaching bit}}$ Within the context of this question if you take tangent of the angle $\theta$ you obtain the value $12.4304$

Writing: ${\tan}^{- 1} \left(12.4304\right)$ means that you are asking: What is the angle whose tangent is 12.4304

Another way of writing $\textcolor{p u r p \le}{{\tan}^{- 1} \left(12.4304\right)} \text{ }$ is $\text{ } \textcolor{p u r p \le}{\arctan \left(\frac{12}{4304}\right)}$

They both mean the same thing. I much prefer the second one as there is no confusion as to what it means when someone first comes across the format ${\tan}^{- 1} \left(12.4304\right)$

They, in error, could think this means $\frac{1}{\tan} \left(12.4304\right)$.

$\textcolor{m a \ge n t a}{\text{IT DEFINITELY DOES NOT MEAN THAT!}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{w h i t e}{}$

$\textcolor{b l u e}{\text{Answering the question}}$

$\textcolor{b r o w n}{\text{What is the value of } \arctan \left(12.4304\right)}$

In this case the tangent is the ratio $\left(\frac{b}{a}\right) \to \frac{12.4304}{1} = 12.4304$

The amount of up or down for the amount of 1 along.

This should sound familiar!

Using the calculator $\arctan \left(12.4304\right) \approx 85.4005781 \ldots . .$

Approximately $85.40$ degrees rounded to 2 decimal places.