#2**+13 **

Best Answer

**atan2(4,3) ?**

$$\mathbf{atan2}{(4,3)}=53.130102354156\ensurement{^{\circ}}\\

\Delta y = 4 \text{ and } \Delta x = 3$$

arctan with two parameters. see **web2.0calculator. **You can input like above.

heureka
Aug 19, 2015

#3**+10 **

In some computer languages atan2(x,y) returns the angle between the origin and point (x,y), with the value returned being between ±180°. In the calculator here, atan2(y,x) returns the angle between (x,y) and the origin.

So here:

$${atan2}{\left(\left({\mathtt{4}}\right), \left({\mathtt{3}}\right)\right)} = {\mathtt{53.130\: \!102\: \!354\: \!156^{\circ}}}$$ This is the angle whose y-component is 4 and whose x-component is 3

However, in Mathcad, for example atan2(4,3) = 36.87° which matches:

$${atan2}{\left(\left({\mathtt{3}}\right), \left({\mathtt{4}}\right)\right)} = {\mathtt{36.869\: \!897\: \!645\: \!844^{\circ}}}$$ This is the angle whose x-component is 4 and whose y-component is 3.

The desired result depends on which is x and which is y. Only the poster will know!

.

Alan
Aug 19, 2015

#5**+5 **

Thank you Alan, that makes good sense. I have not seen it before :))

The numbers being the wrong way around is confusing.

I wonder why Mr Massow did that ? (surely it is not normal)

Melody
Aug 19, 2015

#6**+8 **

**atan2(4,3)**

$$\small{

\begin{array}{lcl}

\tan{(\alpha)} = \frac{a}{b} = \frac{\Delta y}{\Delta x}\\\\

\alpha = \mathbf{atan}{(\frac{a}{b}) }\\\\

\alpha =\mathbf{atan2} { ( a,b) } _{\text{in right quadrant}} =\mathbf{atan2}{ ( \text{numerator},\text{denominator} ) }

=\mathbf{atan2}{ ( \Delta y,\Delta x ) }\\

\end{array}

}$$

heureka
Aug 19, 2015

#7**+5 **

It's not a question of right or wrong, it's just a convention. Mathcad and Excel, for example do it one way; Matlab and webcalc2.0 do it the other way (so Andre Massow is in good company, choosing to do it that way!).

It* is* important to know which convention the piece of software/calculator you are using has chosen, of course!!

.

Alan
Aug 19, 2015

#8**0 **

Thanks Alan, yes it is about convention and now Heureka has explained it I can see that there is a really good reason to do it this way around. Thanks Heureka for explaining it :)

Melody
Aug 19, 2015

#9**+5 **

In general:

The choice of the parametres "a" and "b" determine the angel - orientation:

$$\\\small{\mathrm{atan2}{(\Delta y, \Delta x )} \quad \text{ angle counterclockwise direction start from 'x'-axis }}\\

\small{\mathrm{atan2}{(-\Delta y, \Delta x )} \quad \text{ angle clockwise direction start from 'x'-axis }}\\

\small{\mathrm{atan2}{(\Delta x, \Delta y )} \quad \text{ angle clockwise direction start from 'y'-axis }}\\

\small{\mathrm{atan2}{(-\Delta x, \Delta y )} \quad \text{ angle counterclockwise direction start from 'y'-axis }}\\$$

$$\\\small{\mathrm{atan2}{(\Delta y, -\Delta x )} \quad \text{ angle clockwise direction start from '-x'-axis }}\\

\small{\mathrm{atan2}{(-\Delta y, -\Delta x )} \quad \text{ angle counterclockwise direction start from '-x'-axis }}\\

\small{\mathrm{atan2}{(-\Delta x, -\Delta y )} \quad \text{ angle clockwise direction start from '-y'-axis }}\\

\small{\mathrm{atan2}{(\Delta x, -\Delta y )} \quad \text{ angle counterclockwise direction start from '-y'-axis }}\\$$

heureka
Aug 20, 2015