My Arctangent and Inverse tangent are different

Question

In my computer, using the Genius Math Tool for Ubuntu, the arctangent for (19.62/62.5) comes out as 0.3042. On my calculator the inverse tangent for (19.62/62.5) comes out as 17.428. I am trying to find an angle of the velocities of an object.

Answer 1

Well, the relation between degrees of an angle and radians is given by:

$$x^\circ=x\cdot\frac{\pi}{180}\space\text{radians}\tag1$$

Using radians:

$$\arctan\left(\frac{981}{3125}\right)\approx0.30417801\space\text{radians}\tag2$$

Which is in degrees:

$$\left(\frac{180}{\pi}\cdot\arctan\left(\frac{981}{3125}\right)\right)^\circ\approx17.43^\circ\tag3$$

So, they are equal!

Answer 2

The former is using radians, the latter degrees: $$ \arctan{\left(\frac{19.62}{62.5}\right)} \approx 0.304178 \text{ (radians)} \approx 17.4281^{\circ}. $$