Manual Reference Pages - asind (3fortran)

NAME

ASIND(3) - [MATHEMATICS:TRIGONOMETRIC] Arcsine function in degrees

SYNOPSIS

result = asind(x)

         elemental real(kind=KIND) function asind(x)

          real(kind=KIND) :: x

CHARACTERISTICS

o KIND may be any kind supported by the real type.

o The returned value will be of the same type and kind as the argument.

DESCRIPTION

ASIND(3) computes the arcsine of its argument X in degrees.
The arcsine will allow you to find the measure of a right angle when you know the ratio of the side opposite the angle to the hypotenuse.
The arcsine is the inverse function of the sine function. It is commonly used in trigonometry when trying to find the angle when the lengths of the hypotenuse and the opposite side of a right triangle are known.
Example: ASIND(1.0) has the value 90.0 (approximately).

OPTIONS

o X : The value to compute the arc sine of. The type shall be real and a magnitude that is less than or equal to one |X| <= 1. It is expressed in degrees and lies in the range -90 <= asind(x) <= 90.

RESULT

The result has a value equal to a processor-dependent approximation to arcsin(x).
The result is expressed in degrees and lies in the range
            -90 <= asind (X) <= 90.

EXAMPLES

So if you knew that a train track rose 1.25 vertical miles on a track that was 50 miles long, what is the angle of incline of the track?

The percentage grade is the slope, written as a percent. To calculate the slope you divide the rise by the run. so the slope is 1.25/50 = 0.025. Written as a percent this is 2.5 %.

For the US, 2 1/2 percent, or a rise of 2.5 feet when going 100 feet forward, is generally thought of as the upper limit of the grade on straight track. This was the maximum grade on the first major US railroad, the Baltimore and Ohio. Note curves in the track increase the frictional drag on a train reducing the allowable grade.

Sample program:

    program demo_asind
    use, intrinsic :: iso_fortran_env, only : dp=>real64
    implicit none
    ! value to convert degrees to radians
    real(kind=dp),parameter    :: R2D=180.0_dp/acos(-1.0_dp)
    real(kind=dp)              :: angle, grade, rise, run
    character(len=*),parameter :: all=’(*(g0,1x))’
    integer                    :: i
      ! given sine(theta) = 1.25 miles/50 miles (opposite/hypotenuse)
      ! then taking the arcsine of both sides of the equality yields
      ! theta = arcsine(1.25 miles/50 miles) ie. arcsine(opposite/hypotenuse)
      rise=1.250_dp
      run=50.00_dp
      angle = asind(rise/run)
      print all, ’angle of incline(degrees) = ’, angle
      angle = angle/R2D
      print all, ’angle of incline(radians) = ’, angle
      print all, ’angle of incline(radians) = ’, asin(rise/run)

      print all, ’percent grade=’,rise/run*100.0_dp
      print all,
      do i=-360,360,45
         grade=i/360.0d0
         print *, grade, asind(grade), sind(asind(grade))
      enddo
    end program demo_asind

Results:

> angle of incline(degrees) = 1.4325437375665075 > angle of incline(radians) = 0.25002604899361135E-1 > angle of incline(radians) = 0.25002604899361139E-1 > percent grade= 2.5000000000000000 > > -1.0000000000000000 -90.000000000000000 -1.0000000000000000 > -0.87500000000000000 -61.044975628140158 -0.87500000000000000 > -0.75000000000000000 -48.590377890729144 -0.75000000000000000 > -0.62500000000000000 -38.682187453489441 -0.62500000000000000 > -0.50000000000000000 -30.000000000000004 -0.50000000000000011 > -0.37500000000000000 -22.024312837042164 -0.37500000000000006 > -0.25000000000000000 -14.477512185929925 -0.25000000000000006 > -0.12500000000000000 -7.1807557814582816 -0.12500000000000000 > 0.0000000000000000 0.0000000000000000 0.0000000000000000 > 0.12500000000000000 7.1807557814582816 0.12500000000000000 > 0.25000000000000000 14.477512185929925 0.25000000000000006 > 0.37500000000000000 22.024312837042164 0.37500000000000006 > 0.50000000000000000 30.000000000000004 0.50000000000000011 > 0.62500000000000000 38.682187453489441 0.62500000000000000 > 0.75000000000000000 48.590377890729144 0.75000000000000000 > 0.87500000000000000 61.044975628140158 0.87500000000000000 > 1.0000000000000000 90.000000000000000 1.0000000000000000

STANDARD

Fortran 2023

RESOURCES

o wikipedia: inverse trigonometric functions

Fortran intrinsic descriptions (license: MIT) @urbanjost

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