Question

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

Answer 1

`\tan^{-1}(12.4304)=85.4^\circ`

Explanation:

One can compute `\tan^{-1}(12.4304)` using calculator which gives

`\tan^{-1}(12.4304)=85.4^\circ`

Answer 2

Approximately `85.40` degrees rounded to 2 decimal places.

Explanation:

`color(blue)("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)(12.4304)` means that you are asking: What is the angle whose tangent is 12.4304

Another way of writing `color(purple)(tan^(-1)(12.4304))" "` is `" "color(purple)(arctan(12/4304))`

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)(12.4304)`

They, in error, could think this means `1/tan(12.4304)`.

`color(magenta)("IT DEFINITELY DOES NOT MEAN THAT!")`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(white)()`

`color(blue)("Answering the question")`

`color(brown)("What is the value of "arctan(12.4304))`

In this case the tangent is the ratio `(b/a) -> 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(12.4304)~~85.4005781.....`

Approximately `85.40` degrees rounded to 2 decimal places.