A real life example of the sine function could be a ferris wheel. People board the ride at the ground (sinusoidal axis) and the highest and lowest heights you reach on the ride would be the amplitudes of the graph.
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The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
Waves are periodic function, as is the sine function.
If you mean the sine function, it is dependent on an angle. For example, the sine of an angle of zero degrees is zero; the sine of an angle of 90 degrees is one; for an angle of 180 degrees, the sine is again 0; if you make a graph, you get a curve that looks like a wave. In general, the values the sine function can take are between 1 and -1, inclusive.
Yes, sine is a trig function, it is opposite over hypotenuse.
A sine graph!