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sin.md

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 # Sine
 
-Sine, abbreviated *sin*, is a [trigonometric](trigonometry.md) [function](function.md) that simply said models a smooth oscillation, it is one of the most important and basic functions in geometry, [mathematics](math.md) and [physics](physics.md), and of course in [programming](programming.md). Along with [cosine](cos.md), [tangent](tan.md) and [cotangent](cot.md) it belongs to a group of functions that can be defined by ratios of sides of a right triangle depending on one of the angles in it (hence *trigonometric* -- "triangle measuring"). If some measurement looks like sine function, we say it is *harmonic*. This is very common in nature and technology, e.g. a weight on a spring goes up and down by this function, [alternating current](ac.md) voltage has the sine shape (because it is generated by a circular motion) etc.
+Sine, abbreviated *sin*, is a [trigonometric](trigonometry.md) [function](function.md) that simply said models a smooth oscillation, it is one of the most important and basic functions in geometry, [mathematics](math.md) and [physics](physics.md), and of course in [programming](programming.md). Along with [cosine](cos.md), [tangent](tan.md) and [cotangent](cot.md) it belongs to a group of functions that can be defined by ratios of sides of a right [triangle](triangle.md) depending on one of the angles in it (hence *trigonometric* -- "triangle measuring"). If some measurement looks like sine function, we say it is *harmonic*. This is very common in nature and technology, e.g. a weight on a spring goes up and down by this function, [alternating current](ac.md) voltage has the sine shape (because it is generated by a circular motion), the amount of light falling onto a surface depends on the light angle via sine function etc.
 
 The function is most commonly defined using a right triangle as follows. Consider the following triangle:
 
@@ -16,7 +16,7 @@ The function is most commonly defined using a right triangle as follows. Conside
        b
 ```
 
-*Sin(A)*, where *A* is the angle between side *b* and *c*, is the ratio *a* / *c*. The function can be defined in many other ways, for example it is the curve we get when tracking only one direction (e.g. horizontal) of a point moving alongside circle. It can also be defined as a solution to some [differential equations](differential_equation.md) etc.
+*Sin(A)*, where *A* is the angle between side *b* and *c*, is the ratio *a* / *c*. The function can be defined in many other ways, for example it is the curve we get when tracking only one direction (e.g. horizontal) of a point moving alongside circle (well, in the end it's actually related to the triangle definition) -- imagine something making a circular motion while casting a shadow onto a nearby wall (in a direction that's in the plane of rotation), the shadow will go up and down by sine of time. It can also be defined as a solution to some [differential equations](differential_equation.md) etc.
 
 The graph of the sine function is following:
 
@@ -32,6 +32,8 @@ The graph of the sine function is following:
                -1 |
 ```
 
+Basically we'll observe a sine function in places where something oscillates naturally, gradually, i.e. where something goes there and back repeatedly but in a gradual, smooth manner, slowing down as it's approaching one end, coming to stop for a while, then reversing direction, slowly accelerating the other way and so on. Very rare in nature something comes there and back with constant speed, coming to stop and reversing directions instantly.
+
 **Why the fuck are there these [pi](pi.md) values on the x line???** Nubs often can't comprehend this. These pi values are values in **[radians](radian.md)**, units of measuring angles where *2 pi* is the full angle (360 degrees). In fact sine is sometimes shown with [degrees](degree.md) instead of radians (so imagine 90 degrees on the line where there is 1/2 pi etc.), but mathematicians prefer radians. **But why are there angles in the first place???** Why doesn't it go e.g. from 0 to 1 like all other nice functions? Well, it's because of the relation to geometry, remember the fucking triangle above... also if you define sine with a circle it all repeats after *2 pi*. Just draw some picture if you don't get it.
 
 Some additional facts and properties regarding the sine functions are: