Find the reference angle

Question

This is a fairly simple question. According to this random website I found — Web Archive, a reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. You have to write a program to find these.

I don't remember anything from algebra 2, what does this mean?

Angles are usually given in standard form, which is measured by placing one side of the angle and measuring to the other side, counterclockwise, like so:

This will be your input. Your output will be the reference angle of this. You can think of this as basically the smallest distance from the terminal side to the x-axis. Except it's an angle, not a distance. Here are some examples:

Clarifications

• All the defaults on inputs and submissions.
• Angles is in degrees.
• Negative angles, non-integer angles, and angles > 360 deg are allowed.
• Output in form 60 deg.
• This is code-golf, so shortest code in bytes wins!

Another helpful link.

Test Cases

70      ->  70 deg
135     ->  45 deg
210     ->  30 deg
-60     ->  60 deg
91      ->  89 deg
610     ->  70 deg
-1000   ->  80 deg

Answer 1

Pyth, 17 bytes

+hS%R180,Q_Q" deg

Coincidentally, this is equivalent to @xnor's answer.

Try it online.

Answer 2

Pyth, 18 bytes

+.a-%+QK90yKK" deg

Try it online.

Answer 3

Python 2, 34 bytes

lambda x:`90-abs(x%180-90)`+' deg'

Using "%d deg" string formatting would be longer because of the needed parentheses.

Answer 4

CJam (21 bytes)

180qd1$%z_@@-e<" deg"

Online demo

Answer 5

dc, 25

90?90+d*v180%-d*vn[ deg]p

Note dc uses _ as a -ve sign instead of -.

Test output:

$ for test in 70 135 210 _60 91 610 _1000; do dc -e'90?90+d*v180%-d*vn[ deg]p' <<< $test ; done
70 deg
45 deg
30 deg
60 deg
89 deg
70 deg
80 deg
$

Answer 6

Python 2, 35

lambda x:`min(x%180,-x%180)`+' deg'

The smaller of the angle and its negative modulo 180. Effectively converts the angle to the range from 0 to 180 and takes the distance to the closer of the endpoints. Note that -x%180 groups as (-x)%180.

Same length with string formatting for Python 3:

lambda x:'%d deg'%min(x%180,-x%180)

Answer 7

Mathematica, 22 31

ToString@Abs@Mod[#,180,-90]deg&

Answer 8

Pyth 25 30 bytes

Painfully uncreative solution, using trig functions. Permalink

+.R.t.a.t.t.tQ7Z3 6?%Q1Q0" deg

Any suggestions welcome.

Answer 9

JavaScript (ES6), 43 bytes

Similar to Sp3000's answer, though the modulo is quite lengthy due to the behaviour in JavaScript.

f=x=>90-Math.abs((x%180+180)%180-90)+' deg'

Demo

Code is rewritten in ES5 for browser compatibility:

function f(x){return 90-Math.abs((x%180+180)%180-90)+' deg'}

// Snippet stuff
console.log = function(x){document.body.innerHTML += x + '<br>'};
[70,135,210,-60,91,610,-1000].map(function(v){console.log(f(v))});

CoffeeScript, 45 bytes

f=(x)->90-Math.abs((x%180+180)%180-90)+' deg'

Answer 10

J, 26 bytes

m=:180&|
' deg',~m@-":@<.m

Same as xnor's method.

Answer 11

Matlab, 44

Using an anonymous function:

f=@(x)[num2str(min(mod([x -x],180))) ' deg']

Example:

>> f=@(x)[num2str(min(mod([x -x],180))) ' deg']
f = 
    @(x)[num2str(min(mod([x,-x],180))),' deg']

>> f(70)
ans =
70 deg

>> f(210)
ans =
30 deg

>> f(-1000)
ans =
80 deg

Answer 12

Scala, 40 35 Characters

(a:Int)⇒s"${90-(a%180-90).abs} deg"

Answer 13

Tcl, 83 bytes

proc R a {puts [expr [set a $a%360]>90?$a>180?$a>270?360-$a:$a-180:180-$a:$a]\ deg}

Try it online!

Answer 14

PHP, 44 bytes

Takes one command line parameter. Again PHP suffers from the same issue as JavaScript.

<?=90-abs(($argv[1]%180+180)%180-90)+' deg';

Using the canonical solution requires 53 bytes (the degrees and radians conversion takes a lot of characters):

<?=rad2deg(abs(asin(sin(deg2rad($argv[1])))))+' deg';