In the calculation to change the latitude and longitude to Cartesian (x,y,z) the first step is converting latitude and longitude to Radian. Anyone know why we have to do this and not just use the angles of longitude and latitude?
This is the instruction that i got from one of the reference:
"All latitude and longitude data must be converted into radians. If the coordinates are in degrees.minutes.seconds format, they must first be converted into decimal format. Then convert each decimal latitude and longitude into radians by multiplying each one by PI/180"
Please share if you know why we have to convert the data to rad?
Dear Al Amin, the reason is that Cartesian Coordinates are bind to Latitude and Longitude by formulas where trigonometric functions like Sin(alpha) and Cos(alpha) are used, and angle alpha is by definition measured by radians. Gianluca
Thanks dear Dianluca Argentini,
is that meas, if we use lat and long coordinat by not converting them to radian, it will not work? Please enlight further if possible. thanks again.
Let R the Earth radius and (lat, long) the two angles (lat from equator) in degrees; then x = R cos(long Pi/180) cos(lat Pi/180), y = R sin(long Pi/180) cos(lat Pi/180), z = R sin(lat Pi/180). Gianluca
thanks again and could you suggest me further reading material or help me to understand "angle alpha is by definition measured by radians"? i was thinking that angle also can be measured in degree.
The sin and cos functions usually take angles expressed in radians as input. Although this is merely a convention, its probably a good one because many problems involving angles express those angles most naturally in radians.
Of course, there are many exceptions as well. The MATLAB programming language provides functions sind and cosd that behave exactly like sin and cos but take their inputs in degrees. Apparently the developers of MATLAB believe that angles expressed in degrees come up often enough to justify providing the sind and cosd functions.
The bottom line is that, unless your programming language provides functions like sind and cosd, you will have to convert degrees to radians prior to applying the sin and cos functions.
The link below is a series of short videos that explore the relationship between radians and degrees and beyond.
https://www.brightstorm.com/math/trigonometry/trigonometric-functions/radian-measure-of-angles/
- Badges
- Science topic
- Similar topics
- Mathematics
- Applied Mathematics