What is the relation between trigonometric functions (like) sine and sine waves?

Question

I could never figure this out. The one is used to model and describe relations in a triangle and the other is used to described periodic phenomena.

What is - briefly - the relation?

Most understandable answer wins.

Answer 1

In a right triangle every angle has a sine, it is the ratio of the side opposite the angle in question and the hypotenuse (the long side). A sine wave is just a name for a graph or chart of this value. If you take the sine of every angle from 1 through 360 degrees and plot them on a piece of graph paper you would get a circle, if you shift right one space for each value you will draw a sine wave. 60 cycle AC electric power is often referred to as being a Sine Wave because plotting the voltage of one complete cycle will produce the same graph.

Answer 2

the above purely holds for a stunning-angled triangle, merely as for pythagoras' theorem. The tangent of any attitude is the ratio of the sine of the size of the edge of the triangle at the instant dealing with the attitude and the cosine of the size of the edge of the triangle on the backside of the attitude.