Q&A #193

Teachers' Lounge Discussion: Trigonometry Ratios

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From: shanli

To: Teacher2Teacher Public Discussion
Date: 2001030100:15:28
Subject: negative slope, negative angles, how can that be possible?

Dear Dr. math: when we are exploring the relationships between the angle measures and sides of right triangles, we can develope ratios of the lengths of the sides of similar triangles and called these trigonometric ratios sine, cosine, and tangent, but i don't quite get the process of demonstrating this theory, can you show the demonstration for me plz? Also, it's understood that if the slope of a line is equal to -1 times the slope of the another line, then the slope angle of the first line is equal to -1 times the slope angle of the second line, which means that we will get a negative angle. well,suppose we have right triangle formed by two lines intersecting each other on a coordinate, and one of them has a negative slope and therefore a negative angle. If the question enquired you to get the another angle, the fastest way would be to simply substract the angle we already got from 90 degrees, then it would be like adding those two numbers and resulting in an angle that was more than 90. However, i don't think that generalizing all the angles to be positive as my math pro has suggested, is the right way to solve or comprehend this kind of question. Could you plz give me some hints? Sincerely yours

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