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Thread: What's the idea of trigonometry?

  1. #1 What's the idea of trigonometry? 
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    I'm new to trigonometry, and I want to know if this is right.

    Being used to algebra, the trigonometric functions seem abstract to me since there are no definite operations.

    What I assume: the right triangle model is just a method for defining the functions, correct?

    In the function , if I know then I can solve for like this:

    Pretend is one of the acute angles in the triangle, and what the ratio for opposite to the hypotenuse will just happen to be . Correct?

    So it's not actual operations, just what the ratio will be in this situation?


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  3. #2  
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    What do you mean by "actual operations". When you first get exposed to trigonometry, the definitions are given by these ratios - the only "operation" is division.

    If you start by being given an angle, then you can get the trig functions by constructing a triangle with the given angle, or look the values up in a table. Implicit in this is the elementary geometry theorem that if two triangles are similar, the ratios of the lengths of corresponding sides are the same.


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    I know it involves the divisional operation. I should have worded it better. I meant that trigonometry isn't as direct as simple algebra. I see where I was wrong.

    So never mind about that. Here's my understanding of the method:

    is the ratio of the opposite side to the hypotenuse. Looking at the right triangle model, if I know , then I know all three angle measures.

    Therefore, any triangle with these 3 angle measures is similar (or congruent in one situation) to another triangle with the same angle measures.

    So, if I had a right triangle where degrees, I know

    Since all the triangles are similar, this ratio applies to all sines of . Correct?
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  5. #4  
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    The general idea is correct. However sin(30 deg.) = .5 (exactly).
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  6. #5  
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    Okay thank you. For some reason I had done the secant.
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