# What Does Sin Do To A Number

## Sine is a trigonometric function.

Sine is a trigonometric function. It’s also a periodic function, meaning that the sine of an angle can repeat itself over and over again.

The easiest way to understand this concept is with an example: let’s say we want to calculate the sine of 60 degrees (or π/6 radians). We know that sine is related to sin(θ) = opposite/hypotenuse, so we need to figure out what the opposite and hypotenuse are for 60 degrees. We could start by drawing a right triangle with sides that are 6, 10, and 12 (the triangle’s height), but it turns out there’s a shortcut! We can use our knowledge of trig ratios—or simply memorize them—to make things easier on ourselves:

`sin(60°) = -1/√3 = -1/(√3)*√3 = 1/(√3)`

This tells us that if we multiply both sides by √3 (taking care not to change its value), then dividing by 3 will give us back our original expression for sin(60°). This has been done in step 7 below; notice how everything cancels out except for 1 over 3 (=0.3333…), which means our final answer should be 0.3333…

## What is sin?

Sine is a trigonometric function that evaluates to the ratio of the opposite side of a right-angled triangle to its hypotenuse.

In other words, it tells you how far around the unit circle one should travel in order to get back to your starting point. For example, if you start at 0° and move 2 units around the unit circle (going clockwise), then you have traveled sine(2) units. Sin(0) = 0, sin(1) = 1/2, and so on. If x is equal to something like “the length of string needed to wrap around this spool” then sin(x) will be equal (to some degree of precision) some number between -1 and 1 depending on how many times you need wrap your string around your spool before it reaches its starting point again – i.e., if my string has an odd number of coils then sin((n+1)/2) will be smaller than any positive real number less than one; however if n=4 or 8 or 12 etc., then sin((n+1)/2) will be greater than any positive real number less than one because there are no more integers beyond 4 which can divide into them evenly without leaving anything over when multiplied by 2 and vice versa for odd numbers divisible by two but not four etc…

## What does sin do?

The function sin is a property of all waves. It can be used to find angles and sides of a triangle, which means that it’s part of the trigonometric functions.

## Sine waves are everywhere.

Sine waves are everywhere. They’re in the water, in the light, and in waves of sound; they’re in your ears as you listen to this podcast; they’re even a part of your body’s very structure.

In fact, sine waves are all around us—they’re even outside our galaxy!

## Sin in one dimension.

The sine of an angle is defined as the ratio of the opposite side to the hypotenuse.

It is a periodic function that repeats every 2pi radians or 360°, meaning that sin(x) = x for all values of x where x is in between 0 and 2pi.

## Sin in two and three dimensions.

In two dimensions, sin(x) moves the x coordinate along the unit circle. In three dimensions, sin(x) moves the x, y, and z coordinates of a point along the unit sphere. The unit sphere is a circle in 3D space with radius 1; it looks like this:

![](https://gist.githubusercontent.com/douglascrockford/c8eea6f0ccb79dbf9e08d3507ce88cf5/raw/ac7b62a18fd1ed8ec8c47fd1332bd5ec0799b783/sin_3d_circle_jpegsin_3d_circlejpegFALSEFALSEtrueFALSEtrue)

## The beauty of sin.

The beauty of sin is in its form, which is that of waves. Waves are everywhere and can be seen as the fundamental building blocks of nature, the universe, and life itself. Waves are everywhere: you see them in mountains; you see them in forests; you see them in oceans and rivers.

Waves are what make up your body. You cannot exist without having a wave-like structure to everything about you: your thoughts, your mind, even your very cells themselves!

## Sin and it’s related functions are important properties of all waves

sin, cos and tan are functions of the angle.

If you take the function of an angle in radians and multiply it by 2 pi, you get the same result as multiplying it by 360 degrees. For example: sin(1) = 1*2pi = 2*360degrees . This means that sin(10degrees) is just like 10degrees, except multiplied by pi (pi turns out to be about 3.1415). Since sin(10degrees) equals 10 degrees times pi, then we can write: sin(x)=y where x is any value in radians and y is what happens when we multiply by 3.1415