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JavaScript - Math.acos() method example

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The `Math.acos` function returns number in radians in the range 0 to Math.PI. Based on this function we are able to calculate inverted cosine function value.

``````// ONLINE-RUNNER:browser;

console.log( Math.acos( -2   ) ); // NaN
console.log( Math.acos( -1   ) ); // 3.1415926535897930 ->  180
console.log( Math.acos( -0.5 ) ); // 2.0943951023931957 -> ~120
console.log( Math.acos(  0   ) ); // 1.5707963267948966 ->   90
console.log( Math.acos(  0.5 ) ); // 1.0471975511965979 ->  ~60
console.log( Math.acos(  1   ) ); // 0                  ->    0
console.log( Math.acos(  2   ) ); // NaN

console.log( Math.acos(  0.7071067811865476   ) ); // 0.7853981633974483 -> 45 deg
console.log( Math.acos(  0.8660254037844387   ) ); // 0.5235987755982987 -> 30 deg

console.log(Math.acos( Math.cos(  Math.PI / 4))); // 0.7853981633974483-> pi/4 (45deg)
console.log(Math.cos(  Math.acos( Math.PI / 4))); // 0.7853981633974483-> pi/4 (45deg)``````

Another way to look at `acos` function:

``````// ONLINE-RUNNER:browser;

function calculateAngle(b, h) {
return Math.acos(b / h);
}

/*
|\
| \ h
a |  \
|__*\ <- angle
b
*/

var a, b, h;

// a, b and h build isosceles right triangle
a = 3;
b = a;
h = Math.sqrt(a * a + b * b);
console.log( calculateAngle(b, h) ); // 0.7853981633974483 <-  45 degrees

// a, b and h build half of equilateral triangle
a = 3;
b = a * Math.sqrt(3);
h = Math.sqrt(a * a + b * b);
console.log( calculateAngle(b, h) ); // 0.5235987755982987 <- ~30 degrees

// a, b and h are not able to build triangle
a = 3;
b = a;
h = 1;
console.log( calculateAngle(b, h) ); // NaN``````

1. Documentation

 Syntax `Math.acos(number)` Parameters `number` - integer or float number value that represents result of operation `adjacent / hypotenuse` on right triangle (primitive value). `number` should be in the range `-1` to `+1`. Result `number` value in radians in the range `0` to `Math.PI` (primitive value). If value can not be calculated `NaN` is returned. Description `acos` is a static method that takes only one parameter and returns an approximation of the result of the mathematical function arccosine(x).

2. Working with degrees

``````// ONLINE-RUNNER:browser;

function calculateAngle(b, h) {
var angle = Math.acos(b / h);

return (180 / Math.PI) * angle; // rad to deg conversion
}

/*
|\
| \ h
a |  \
|__*\ <- angle
b
*/

var a, b, h;

// a, b and h build isosceles right triangle
a = 3;
b = a;
h = Math.sqrt(a * a + b * b);
console.log( calculateAngle(b, h) ); // 45 degrees

// a, b and h build half of equilateral triangle
a = 3;
b = a * Math.sqrt(3);
h = Math.sqrt(a * a + b * b);
console.log( calculateAngle(b, h) ); // ~30 degrees

// a, b and h are not able to build triangle
a = 3;
b = a;
h = 1;
console.log( calculateAngle(b, h) ); // NaN``````

3. Canvas plot example

``````// ONLINE-RUNNER:browser;

<!doctype html>
<html>
<style> #canvas { border: 1px solid black; } </style>
<body>
<canvas id="canvas" width="200" height="200"></canvas>
<script>

var canvas = document.querySelector('#canvas');
var context = canvas.getContext('2d');

// arccosine chart range
var x1 = -1.0;
var x2 = +1.0;
var y1 =  0;
var y2 = +Math.PI

var dx = 0.01;

var xRange = x2 - x1;
var yRange = y2 - y1;

function calculatePoint(x) {
var y = Math.acos(x);

// chart will be reversed horizontaly because of reversed canvas pixels

var nx = (x - x1) / xRange;       // normalized x
var ny = 1.0 - (y - y1) / yRange; // normalized y

var point = {
x: nx * canvas.width,
y: ny * canvas.height
};

return point;
}

console.log('x range: <' + x1 + '; ' + x2 + '>');
console.log('y range: <' + y1 + '; ' + y2 + '> // angles in radians');

var point = calculatePoint(x1);

context.beginPath();
context.moveTo(point.x, point.y);

for (var x = x1 + dx; x < x2; x += dx) {
point = calculatePoint(x);
context.lineTo(point.x, point.y);
}

point = calculatePoint(x2);
context.lineTo(point.x, point.y);
context.stroke();

</script>
</body>
</html>``````

References

1. Inverse trigonometric functions - Wikipedia

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