Manual Reference Pages - asin (3)

NAME

asin(3f) - [FORTRAN:INTRINSIC:MATHEMATICS:TRIGONOMETRIC] Arcsine function

SYNTAX

result = asin(X)

DESCRIPTION

asin(x) computes the arcsine of its argument X.
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.

ARGUMENTS

X The type shall be either REAL and a magnitude that is less than or equal to one; or be COMPLEX.

RETURN VALUE

RESULT The return value is of the same type and kind as X. The real part of the result is in radians and lies in the range -PI/2 <= asin(x) <= PI/2.

EXAMPLE

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.

So if you knew that a train track rose 1.25 vertical miles on a track that was 50 miles long, you could determine the average angle of incline of the track using the arcsine. Given

    sin(Θ) = 1.25 miles/50 miles (opposite/hypotenuse)

    program demo_asin
    use, intrinsic :: iso_fortran_env, only : dp=>real64
    implicit none
    ! value to convert degrees to radians
    real(kind=dp),parameter :: D2R=acos(-1.0_dp)/180.0_dp
    real(kind=dp)           :: angle, rise, run
      ! given sine(Θ) = 1.25 miles/50 miles (opposite/hypotenuse)
      ! then taking the arcsine of both sides of the equality yields
      ! Θ = arcsine(1.25 miles/50 miles) ie. arcsine(opposite/hypotenuse)
      rise=1.250_dp
      run=50.00_dp
      angle = asin(rise/run)
      write(*,*)’angle of incline(radians) = ’, angle
      angle = angle/D2R
      write(*,*)’angle of incline(degrees) = ’, angle

      write(*,*)’percent grade=’,rise/run*100.0_dp
    end program demo_asin

Results:

    angle of incline(radians) =    2.5002604899361139E-002
    angle of incline(degrees) =    1.4325437375665075
    percent grade=   2.5000000000000000

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

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

STANDARD

[[FORTRAN 77]] and later, for a complex argument [[Fortran 2008]] or later

CLASS

[[Elemental procedure|Elemental function]]

JSU

asin (3)

March 11, 2021

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