# Convert from spherical angles to longitude and latitude

I have some images extracted from a radar from Austria and a formula for the projections (the exercice says The projection formulas map pixel locations to geographical coordinates), that transforms pixels into `(phi, lambda)` which the exercise states that are the spherical angles.

``````PRODUCT-PH-FORMS   =     "(1.570796326795-2*atan(0.404026225835*pow((1/sin(acotan(5899179.2/\
((5676531.8*pow((tan((1.570796326795-(v1*0.017453292520))/2)/\
0.373884679485),0.737361597616)*sin(0.012869387656*(v0-13.333333333))-\
v3*v4)+COL*v4)-((6380000.0*(0.924636243305-0.889738536848*pow((tan((\
1.570796326795-(v1*0.017453292520))/2)/0.373884679485),0.737361597616)*\
cos(0.012869387656*(v0-13.333333333)))+v2*v5)-ROW*v5)/((5676531.8*\
pow((tan((1.570796326795-(v1*0.017453292520))/2)/0.373884679485),\
0.737361597616)*sin(0.012869387656*(v0-13.333333333))-v3*v4)+COL*v4))))*\
((5676531.8*pow((tan((1.570796326795-(v1*0.017453292520))/2)/\
0.373884679485),0.737361597616)*sin(0.012869387656*(v0-13.333333333))-\
v3*v4)+COL*v4)/6380000.0*0.737361597616/sin(0.767944870878),1/\
0.737361597616)))"

PRODUCT-LA-FORMS   = f(pixel row, pixel col, v0, v1, v2, v3, v4, v5)
``````

But this gives very small values which cannot be `(latitude, longitude)` so I am looking for the transformation between spherical angles `(phi,lambda)` to `(latitude,longitude)`

For the result I need to provide `(latitude, longitude)` so how this conversion could be made? The exercise provides me as well with some data I do not understand, which may be necessary:

``````v0=8.194 (reference lon)
v1=50.437 (reference lat)
v2 = 0
v3 = 0
v4=1018.18 (meter / pixel)
v5=1018.18 (meter / pixel)
``````

This variables are used for the transformation formulas but may be useful as well to obtain `(latitude, longitude)`

## EDIT

I have tried to directly consider the values I obtain from the transformation as (latitude, longitude) after `*180/pi` but the coordinates I get are not in Austria

• Hi Victor, welcome to GIS SE! Usually, phi is the Greek letter that we call latitude, and lambda is the Greek letter that we call longitude. In the event that you are exercising spherical trigonometry, these are spherical angles. I think you are feeling a bit overwhelmed by the practical problem because you don't have the previous theoretical concepts. Study the theory and if you cannot interpret the problem, present the complete excercise and ask for help in its interpretation. Jun 6, 2020 at 1:05
• Hey Gabriel, they have told me these are spherical angles so how could I do the conversion to latitude, longitude? Or you could point me out to a resource as well, thanks a lot Jun 6, 2020 at 5:55
• @GabrielDeLuca have edited the question to see whether is more clear now Jun 6, 2020 at 6:30
• The formula looks like it is converting degrees for input into radians for the trig functions, since the constants 0.01745329 = pi/180 and 1.570796 = pi/2 are frequent. Do the trig functions in whatever you are using expect Radians or Degrees for their inputs? If there's a mis-match it could be very wrong. Nov 9, 2020 at 16:54

``````  * ( 180 / Pi )