cos

A function that can be used in Formulas.

## Syntax and semantics

`cos` (`x`)
  compute the cosine of `x`.

`Axes: -5, 5, -1.1, 1.1
` `Draw inner box
` `Draw function: -5, 5, 1000, ~ cos (x)
` `One mark bottom: -3*pi/2, "no", "yes", "yes", "\-m3%\pi/2"
` `One mark bottom: -pi, "no", "yes", "yes", "\-m%\pi"
` `One mark bottom: -pi/2, "no", "yes", "yes", "\-m%\pi/2"
` `One mark bottom: 0, "no", "yes", "yes", "0"
` `One mark bottom: pi/2, "no", "yes", "yes", "+%\pi/2"
` `One mark bottom: pi, "no", "yes", "yes", "+%\pi"
` `One mark bottom: 3*pi/2, "no", "yes", "yes", "+3%\pi/2"
` `One mark left: -1, "no", "yes", "yes", "\-m1"
` `One mark left: 0, "no", "yes", "yes", "0"
` `One mark left: 1, "no", "yes", "yes", "+1"
` `Text bottom: "yes", "%x \->"
` `Text left: "yes", "##cos# (%x)"
` `Text top: "no", "##just over one and a half periods of a (co)sine wave"
`

This picture illustrates the following properties of the cosine function:

  • `cos` (x) is zero for all values of x that are odd multiples of π/2.
  • The extrema of `cos` (x) are −1 and +1.
  • `cos` (x) is −1 or +1 wherever x is an integer multiple of π.
  • The cosine function is periodic with period 2π, i.e., `cos` (x+2π) = `cos` (x).
  • The cosine function is symmetric around 0, i.e. `cos` (−x) = `cos` (x).
  • The cosine function is antisymmetric around π/2, i.e. `cos` (π/2−x) = − `cos` (x); in other words, if you take the cosine curve and rotate it by 180 degrees around the point (π/2, 0), then you get the same curve again.

A cosine wave is a special case of the more general sine wave that is given by y = `sin` (x + φ), where φ (an additive constant called the initial phase) is π/2.

### Links to this page

- `cos##`
- `cos#`
- Functions