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?
Best Answer
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.