Finding the angle between two bearings is often confusing.[1]



Task

Find the angle which is the result of the subtraction b2 - b1, where b1 and b2 are the bearings.


Input bearings are expressed in the range   -180   to   +180   degrees.

The  result  is also expressed in the range   -180   to   +180   degrees.



Compute the angle for the following pairs:

 20 degrees (b1) and 45 degrees (b2)
 -45 and 45
 -85 and 90
 -95 and 90
 -45 and 125
 -45 and 145
 29.4803 and -88.6381
 -78.3251 and -159.036


Optional extra
 
Allow the input bearings to be any (finite) value.



Test cases

 -70099.74233810938 and 29840.67437876723
 -165313.6666297357 and 33693.9894517456
 1174.8380510598456 and -154146.66490124757
 60175.77306795546 and 42213.07192354373


#lang racket
(define (% a b) (- a (* b (truncate (/ a b)))))
 
(define (bearing- bearing heading)
  (- (% (+ (% (- bearing heading) 360) 540) 360) 180))
 
(module+ main
  (bearing- 20 45)
  (bearing- -45 45)
  (bearing- -85 90)
  (bearing- -95 90)
  (bearing- -45 125)
  (bearing- -45 145)
  (bearing- 29.4803 -88.6381)
  (bearing- -78.3251 -159.036)
 
  (bearing- -70099.74233810938 29840.67437876723)
  (bearing- -165313.6666297357 33693.9894517456)
  (bearing- 1174.8380510598456 -154146.66490124757)
  (bearing- 60175.77306795546 42213.07192354373))
 
(module+ test
  (require rackunit)
 
  (check-equal? (% 7.5 10) 7.5)
  (check-equal? (% 17.5 10) 7.5)
  (check-equal? (% -7.5 10) -7.5)
  (check-equal? (% -17.5 10) -7.5))