The document discusses the difference between the atan and atan2 functions. Atan returns the principal value of the arctangent of y/x in radians between -π/2 and π/2. Atan2 avoids problems when determining the quadrant by also considering the signs of both x and y, allowing it to return values between -π and π. Some examples are provided where atan and atan2 return different values due to the quadrant. The document recommends checking the man pages for more details on atan and atan2.

1. Atan2 function
Colin Cheng ( 鄭聖文 )
Shengwen1997.tw@gmail.com

2. Brief explanation about the difference
between atan and atan2.

3. Just a normal example
x
y
1
1
θ
(1,1)=[√2, π
4
]
θ=atan(
y
x
)
θ=atan(
1
1
)= π
4

4. Next example
1
-1
θ
θ=atan(
y
x
)
θ=atan(
−1
1
)=atan(−1)=−π
4

5. What if...
1
-1
θ
θ=atan(
y
x
)
θ=atan(
−1
1
)=atan(−1)=−π
4
θ=atan(
1
−1
)=atan(−1)=−π
4
1
-1
Avoid the preoblem
by using atan2!

6. Atan2
atan2( y , x)=
atan( y/x) for x>0
atan( y/x)+π for x<0, y≥0
atan( y/x)−π for x<0, y<0
π/2 for x=0 , y>0
−π/2 for x=0, y<0
undefined for x=0, y=0

7. Type “man atan” and “man atan2” under
Linux to get the detailed description.