ATAN2
The function atan2(y,x) is defined as:
atan2(y,x) = tan^-1 (y/x) with respect to the quadrant the point (x, y) is in. In case you didn't know, with respect to point (x, y):
(x, y) is in Quadrant I if x > 0 and y > 0
(x, y) is in Quadrant II if x < 0 and y > 0
(x, y) is in Quadrant III if x < 0 and y < 0
(x, y) is in Quadrant IV if x > 0 and y < 0
Visually:
This is different from the two common calculator functions used to find the arctangent: Arctangent and Argument.
The Arctangent Function
TI and Casio Calculators*: tan^-1(y/x)
Hewlett Packard Calculators*: atan (y/x)
* The majority of them
Range (Output): -90° to 90°, -π/2 to π/2 radians
How to use Arctangent to get atan(y,x)
If the point is in quadrant I:
Use atan(y/x)
If the point is in quadrant II or III:
Use atan(y/x) + 180° in degrees mode
Use atan(y/x) + π in radians mode
If the point is in quadrant IV:
Use atan(y/x) + 360° in degrees mode
Use atan(y/x) + 2*π in radians mode
Special cases have to be used x or y is equal to 0:
If x=0 and y<0, the angle is 270° (3*π/2 radians)
If x=0 and y>0, the angle is 90° (π/2 radians)
If y=0 and x<0, the angle is 180° (π radians)
If y=0 and x>0, the angle is 360° or 0° (2*π or 0 radians)
The Argument Function
The complex number x + yi is used.
TI Calculators: angle(x + y*i)
Casio and Hewlett Packard Calculators: ARG(x + y*i)
Range: -180° to 180°, -π to π radians
How to use the Argument function to get atan2(y,x)
This is a great way to get atan2, which cleverly makes the use of complex numbers. In addition, there are a lot fewer things to remember:
If y≥0 (Quadrants I and II):
Use ARG(x+yi)*
(*The angle function if you are using a TI calculator)
If y<0 (Quadrants III and IV):
Use ARG(x+yi) + 360° for degrees mode
Use ARG(x+yi) + 2*π for radians mode
I hope this tip is helpful. Happy Thanksgiving and I am very thankful for all who have read, followed, and supported my blog over the last two years.
Eddie
This blog is property of Edward Shore. 2013