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Q&A #193

Teachers' Lounge Discussion: Trigonometry Ratios

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From: shanli <shanliliu@yahoo.com>
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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