sin

A function that can be used in Formulas.

## Syntax and semantics

`sin` (`x`)
  compute the sine of `x`.

`Axes: -5, 5, -1.1, 1.1
` `Draw inner box
` `Draw function: -5, 5, 1000, ~ sin (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", "##sin# (%x)"
` `Text top: "no", "##just over one and a half periods of a sine wave"
`

This picture illustrates the following properties of the sine function:

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

### Links to this page

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