# Why arctan in radian mode and arctan in degrees mode are different?

So I've been playing around with my calculator.

In degrees mode with my casio calculator, I typed, "$$\arctan(1)$$" and got an answer of 45.

In radian mode with the same parameter, I got, "0.785398..."

So I'm thinking like, "If you can convert degrees to radian in sin(x) by multiplying x with $$\frac{180}{\pi}$$, it should work with arctan", but when I tried in degrees mode with the parameter $$\arctan(\frac{180}{\pi})$$, it gave me "89.0001..." which is far from the correct value of "0.785398...".

Where did I went wrong?

In degrees mode, $$\arctan(1) = 45^{\circ}$$. So, if you want this in radians, you need to convert $$45^{\circ}$$ to radians, if you do so, you get $$0.785$$, as expected.
One way to think of this is that the thing which is in degrees/radians is the angle; i.e the thing which you input into the trigonometric functions $$\sin(\cdot), \cos(\cdot), \tan(\cdot), \csc(\cdot), \sec(\cdot), \cot(\cdot)$$, NOT their inverses. If you look at the inverse functions then it is the output which is an angle.
The output of $$\arctan(1)$$ is the angle, not the input.
Put the calculator in radian mode and write $$\frac{180}{\pi}\arctan(1)$$ to see what you get.