Monday, 16 March 2009

How to make a sine wave

If you have learned SOH CAH TOA then you know about the theoretical mathematics of right-angles. Now think of the practical aspect to this mathematics and think of a ladder on the floor touching a wall. The sine tells us how high the ladder is up the wall, as it tells us about the opposite side in the triangle (the wall). The sine of 0 degrees is zero. As you pick up the ladder and slide it up the wall, the hypotenuse is always the length of the ladder, but the height is gradually increased to a maximum when the ladder is vertical (90 degrees). Then the length of the hypotenuse is the same as the opposite. The sine is the opposite / adjacent, and the sine of 90 degrees (usually abbreviated to sin 90) is 1.

The sine of 90 degrees is 1 because it is a matter of convention that the ladder has a length of one unit. You could have different lengths but it makes sense to choose something simple. This means that the sin 0 is zero, as the ladder is not up the wall at all, and the sin 90 is 1. Continue to move the ladder without changing direction so that it is coming back to the floor behind you. The sin 180 is zero. If you can imagine the ladder in mid-air, say hanging by a crane, then at 180 + 90 = 270 degrees the ladder is hanging vertically downwards. The sin 270 is -1. When you get to 360 degrees you are back where you started. Sin 360 is zero. If you plot the height of the ladder from 0 to 360 degrees on a graph then you end up with a sine wave.

That sums it up.

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