Manual Reference Pages  - sin (3fortran)

NAME

SIN(3) - [MATHEMATICS:TRIGONOMETRIC] Sine function

SYNOPSIS

result = sin(x) 

         elemental TYPE(kind=KIND) function sin(x)


          TYPE(kind=KIND) :: x

CHARACTERISTICS

o X may be any real or complex type
o KIND may be any kind supported by the associated type of X.
o The returned value will be of the same type and kind as the argument X.

DESCRIPTION

SIN(3) computes the sine of an angle given the size of the angle in radians.

The sine of an angle in a right-angled triangle is the ratio of the length of the side opposite the given angle divided by the length of the hypotenuse.

OPTIONS

o X : The angle in radians to compute the sine of.

RESULT

The return value contains the processor-dependent approximation of the sine of X

If X is of type real, it is regarded as a value in radians.

If X is of type complex, its real part is regarded as a value in radians.

EXAMPLES

Sample program: 

    program sample_sin
    implicit none
    real :: x = 0.0
       x = sin(x)
       write(*,*)’X=’,x
    end program sample_sin
Results: 

     >  X=  0.0000000E+00
Extended Example

Haversine Formula

From the article on "Haversine formula" in Wikipedia: 

       The haversine formula is an equation important in navigation,
       giving great-circle distances between two points on a sphere from
       their longitudes and latitudes.
So to show the great-circle distance between the Nashville International Airport (BNA) in TN, USA, and the Los Angeles International Airport (LAX) in CA, USA you would start with their latitude and longitude, commonly given as 

      BNA: N 36 degrees 7.2’,   W 86 degrees 40.2’
      LAX: N 33 degrees 56.4’,  W 118 degrees 24.0’
which converted to floating-point values in degrees is:
o BNA latitude=36.12, longitude=-86.67
o LAX latitude=33.94, longitude=-118.40

And then use the haversine formula to roughly calculate the distance along the surface of the Earth between the locations:

Sample program: 

    program demo_sin
    implicit none
    real :: d
        d = haversine(36.12,-86.67, 33.94,-118.40) ! BNA to LAX
        print ’(A,F9.4,A)’, ’distance: ’,d,’ km’
    contains
    function haversine(latA,lonA,latB,lonB) result (dist)
    !
    ! calculate great circle distance in kilometers
    ! given latitude and longitude in degrees
    !
    real,intent(in) :: latA,lonA,latB,lonB
    real :: a,c,dist,delta_lat,delta_lon,lat1,lat2
    real,parameter :: radius = 6371 ! mean earth radius in kilometers,
    ! recommended by the International Union of Geodesy and Geophysics


    ! generate constant pi/180
    real, parameter :: deg_to_rad = atan(1.0)/45.0
       delta_lat = deg_to_rad*(latB-latA)
       delta_lon = deg_to_rad*(lonB-lonA)
       lat1 = deg_to_rad*(latA)
       lat2 = deg_to_rad*(latB)
       a = (sin(delta_lat/2))**2 + &
              & cos(lat1)*cos(lat2)*(sin(delta_lon/2))**2
       c = 2*asin(sqrt(a))
       dist = radius*c
    end function haversine
    end program demo_sin
Results: 

     > distance: 2886.4446 km

STANDARD

FORTRAN 77

SEE ALSO

ASIN(3), COS(3), TAN(3), ACOSH(3), ACOS(3), ASINH(3), ATAN2(3), ATANH(3), ACOSH(3), ASINH(3), ATANH(3)

RESOURCES

o Wikipedia:sine and cosine
Fortran intrinsic descriptions (license: MIT) @urbanjost

Nemo Release 3.1 sin (3fortran) November 02, 2024
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