Deriving Basic (Circular) Trigonometric Functions

Mathematics, Physics
[caption id="attachment_18674" align="alignright" width="401"] Figure 1[/caption] Draw two intersecting lines in space, illustrated below. The mathematician will not want to leave this simple drawing without completely pointing out its features and labeling those features. We do so to begin our understanding of basic (circular) trigonometric functions. [caption id="attachment_18675" align="alignleft" width="387"] Figure 2[/caption] We label the point of intersection of course – P will do. But the intersection produces what looks like slices in a pie. The size of those slices of pie were determined by how the two lines intersected, how "wide apart" the lines are. We label these as angles α (alpha) and β (beta). Superimposing a Circle [caption id="attachment_18676" align="alignright" width="387"] Figure 3[/caption] The title of this paper is understanding basic circular trigonometric functions. So at this stage,…
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Mathematical Equation for a Cone

You go to the mall and request a double scoop of Rocky Road ice cream. The fellow serving says "Yes," and then he asks you asks if you would like that on a wafer or a sugar cone? Since most have eaten ice cream since childhood (unless we are dairy or otherwise intolerant), the majority of people think of a simple v-shape hollow structure as a cone. It has a top. It has a bottom. But is this the kind of geometrical shape that mathematicians think of when they refer to deriving the mathematical equation of a cone? A Mathematics Cone The cone of the mathematician bears some resemblance to that, but there are differences. The figure included with this article demonstrates that there are two v-shaped portions, not one.…
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