Length of an arc between two angles

Task

Write a method (function, procedure etc.) in your language which calculates the length of the major arc of a circle of given radius between two angles.

In this diagram the major arc is colored green.

Illustrate the use of your method by calculating the length of the major arc of a circle of radius 10 units, between angles of 10 and 120 degrees.

Factor

<lang factor>USING: kernel math math.constants math.trig prettyprint ;

arc-length ( radius angle angle -- x )

   - abs deg>rad 2pi swap - * ;

10 10 120 arc-length .</lang>

Output:

43.63323129985824

Go

Translation of: Julia

<lang go>package main

import (

   "fmt"
   "math"

)

func arcLength(radius, angle1, angle2 float64) float64 {

   return (360 - math.Abs(angle2-angle1)) * math.Pi * radius / 180

}

func main() {

   fmt.Println(arcLength(10, 10, 120))

}</lang>

Output:

43.63323129985823

The task seems to be to find the distance along the circumference of the circle which is NOT swept out between the two angles. <lang julia> arclength(r, angle1, angle2) = (360 - abs(angle2 - angle1)) * π/180 * r @show arclength(10, 10, 120) # --> arclength(10, 10, 120) = 43.63323129985823 </lang>

Phix

Translation of: Julia

<lang Phix>function arclength(atom r, angle1, angle2)

   return (360 - abs(angle2 - angle1)) * PI/180 * r

end function ?arclength(10, 10, 120) -- 43.6332313</lang>

Raku

Works with: Rakudo version 2020.02

<lang perl6>sub arc ( \r, \a1, \a2 ) { r × (τ - abs(a2 - a1)) } sub postfix:<°> (\d) { d × τ / 360 }

say arc(10, 10°, 120°), ' engineering units';</lang>

Output:

43.63323129985824 engineering units

REXX

Translation of: Julia

This REXX version handles angles (in degrees) that may be > 360º. <lang rexx>/*REXX program calculates the length of an arc between two angles (stated in degrees).*/ parse arg radius angle1 angle2 . /*obtain optional arguments from the CL*/ if radius== | radius=="," then radius= 10 /*Not specified? Then use the default.*/ if angle1== | angle1=="," then angle1= 10 /* " " " " " " */ if angle2== | angle2=="," then angle2= 120 /* " " " " " " */

say ' circle radius = ' radius say ' angle 1 = ' angle1"º" /*angles may be negative or > 360º.*/ say ' angle 2 = ' angle2"º" /* " " " " " " " */ say say ' arc length = ' arcLength(radius, angle1, angle2) exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ arcLength: procedure; parse arg r,a1,a2; #=360; return (#-abs(a1//#-a2//#)) * pi()/180 * r /*──────────────────────────────────────────────────────────────────────────────────────*/ pi: pi= 3.1415926535897932384626433832795; return pi /*use 32 digs (overkill).*/</lang>

output when using the default inputs:

     circle radius =  10
           angle 1 =  10º
           angle 2 =  120º

        arc length =  43.6332313

zkl

Translation of: Julia

<lang zkl>fcn arcLength(radius, angle1, angle2){

  (360.0 - (angle2 - angle1).abs()).toRad()*radius

} println(arcLength(10,10,120));</lang>

Output:

43.6332