cos()

The cos(angle) function accepts only one value as its parameter.

angle

A calculation which resolves to a <number> or an <angle>. When specifying unitless numbers they are interpreted as a number of radians, representing an <angle>.

The cosine of an angle will always return a number between −1 and 1.

• If angle is infinity, -infinity, or NaN, the result is NaN.

<cos()> = 
  cos( <calc-sum> )  

<calc-sum> = 
  <calc-product> [ [ '+' | '-' ] <calc-product> ]*  

<calc-product> = 
  <calc-value> [ [ '*' | '/' ] <calc-value> ]*  

<calc-value> = 
  <number>         |
  <dimension>      |
  <percentage>     |
  <calc-constant>  |
  ( <calc-sum> )   

<calc-constant> = 
  e          |
  pi         |
  infinity   |
  -infinity  |
  NaN        

The cos() function can be used to keep the size of a rotated box.

When the element is rotated using rotate(), it goes beyond its initial size. To fix this, we will use cos() to update the element size.

For example, if you rotate a 100px/100px square 45deg, the diamond it creates will be wider and taller than the original square. To shrink the diamond into the box allotted for the original square, you would have to scale down the diamond using this formula: width = height = 100px * cos(45deg) = 100px * 0.707 = 70.7px. You need to also adjust the transform-origin and add translate() to correct the position:

HTML

<div class="original-square"></div>
<div class="rotated-diamond"></div>
<div class="rotated-scaled-diamond"></div>

CSS

body {
  height: 100vh;
  display: flex;
  justify-content: center;
  align-items: center;
  gap: 50px;
}

div.original-square {
  width: 100px;
  height: 100px;
  background-color: blue;
}
div.rotated-diamond {
  width: 100px;
  height: 100px;
  background-color: red;
  transform: rotate(45deg);
}
div.rotated-scaled-diamond {
  width: calc(100px * cos(45deg));
  height: calc(100px * cos(45deg));
  margin: calc(100px / 4 * cos(45deg));
  transform: rotate(45deg);
  transform-origin: center;
  background-color: green;
}

Result

• sin()
• tan()
• asin()
• acos()
• atan()
• atan2()