If you are looking at a right triangle from the point of view of one of the small angles, the sine is the ratio of the side opposite the angle to the hypotenuse (side opposite the right angle) of the triangle. The graph of the sine of the angle starts at zero, smoothly increases to 1, smoothly decreases past zero to minus 1 then smoothly increases to zero and does this over and over forever. This curve describes the height of a spot on the circumference of a spinning wheel and many other physical phenomena that involve rotation.
If you put a coefficient in front of the sine function, it changes the minimum and maximum values of the function but does nothing to change the period of the function. For example Y = 3 Sin A oscillates between -3 and +3 but crosses the X axis at the same places as Y = Sin A and goes through the same number of cycles in the same amount of time.
The other way to manipulate the sine function is to put a constant in front of the angle instead of in front of the sine. This looks like Y = Sin nA, where n is the constant and A is the angle. This manipulation changes the period instead of the amplitude like Y = n Sin A. So Y = Sin nA manipulates the frequency of Y = Sin A and Y = n Sin A manipulates the amplitude of Y = Sin A.
By combining these two manipulations, you can approximate other periodic functions by selectively adding combinations of sines. Consider the sequence A1 Sin X + A2 Sin 2X + A3 Sin 3X + A4 Sin 4X + ... and so on. The sequence of Numbers A1, A2, A3, ... and so on can be chosen to selectively emphasize and de-emphasize the different sine frequencies. This sequence of numbers describes the periodic function being approximated.
The sequence A1, A2, A3, ... and so on can only be used to approximate periodic functions that start at zero. Combine the sequence with a similar series of cosines can, however, approximate any periodic function. The sequence A1 Sin X + B1 Cos X + A2 Sin 2X + B2 Cos 2X +A3 Sin 3X + B3 Cos 3X + ... and so on can approximate any periodic function. The first few A's and B's are usually enough to approximate any function close enough.