Trig Based on the Unit SquareDate: 10/22/98 at 10:31:28 From: ben barr Subject: Trig Hi, Lately, this question has been puzzling me. Why are the sine and cosine graphs defined in a unit circle? Why not a unit square or any other geometric shape? Thanks for your time! I hope to hear back soon. Date: 10/22/98 at 21:46:23 From: Doctor Sam Subject: Re: Trig Ben, That is really a fabulous question! You can certainly define things like the sine and the cosine using a unit square (or an ellipse or a rectangle, or any other geometric figure). It's fun to see what some of them look like. For example, if you draw a unit square from (1,0) to (1,1) to (0,1) to (0,0) and graph the y-coordinate as you move around the square counter-clockwise you will get something very similar to the graph y = sin x, except it will be made up of straight line segments rather than a smooth curve. But the reason that the trig functions are defined using the unit circle is that scientists often want to describe circular motion (like planets around the sun or satellites around the Earth). The trig functions are easy to use for this purpose because they have circular motion built into their definitions. Of course, the trig functions aren't used only to describe motion around a circle, but it turns out that they are very useful when describing anything that repeats periodically, and many things in nature occur in cycles. I hope that helps. - Doctor Sam, The Math Forum http://mathforum.org/dr.math/ |
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