Henry D.

asked • 07/09/21

What is the purpose of the division of two lengths of a triangle in Trigonometry?

 I understand the definitions of the six trigonometric functions but I don't understand why do we use the operation division for two lengths of a triangle. My teacher said that "it's just a rule" but it's more than a rule, there has to be meaning and purpose for the division of the trigonometric functions.

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Brent K. answered • 07/09/21

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Hi Henry,


Someone else could possibly provide further context, but the reason, as I see it, is due to similar triangles - similar triangles have side ratios (i.e. the result of division) that are the same, and it's this fact that even lets us define the trig functions of an angle to begin with

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Andrew D.

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I concur with this 100%. The whole point of defining trigonometric functions using ratios of sides is to relate the angles of triangles to the sides. By this relation, any triangle with the same indicated angle and ratio between sides must be similar. This allows for generalization (so we can compute values for any similar triangle, not just a specific one).
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07/09/21

Mark M.

A distinction must be made between right-triangle trigonometry (to which you refer) and trigonomtric functions.
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07/10/21

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