- #1

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sin theta = opposite side / hypotenuse

cos theta = adjacent side / hypotenuse

tan theta = opposite side / adjacent side.

But why? Are there some explanations behind or are they just defined by scientists?

- Thread starter iknownth
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- #1

- 16

- 0

sin theta = opposite side / hypotenuse

cos theta = adjacent side / hypotenuse

tan theta = opposite side / adjacent side.

But why? Are there some explanations behind or are they just defined by scientists?

- #2

pwsnafu

Science Advisor

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What do you mean by "explanations"?But why? Are there some explanations behind or are they just defined by scientists?

To answer the question, they are the definitions used in planar geometry. There are other (equivalent) ways of defining them, but you'll get the same properties nonetheless.

- #3

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How can one prove that sin theta = opposite side / hypotenuse ?

- #4

pwsnafu

Science Advisor

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I'm assuming planar geometry here. There are two answers:How can one prove that sin theta = opposite side / hypotenuse ?

- It
*is*the definition of sine. There is nothing to prove. - The definition is using the unit circle. It which case the proof is immediate from similar triangles.

I guess it's worth asking: what is

- #5

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In this case, there is still something to prove. You want to prove also that if two triangles have the same angle, then the quantity opposite side/hypothenuse is the same.Itisthe definition of sine. There is nothing to prove.

- #6

pwsnafu

Science Advisor

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Arrgh yes of course.In this case, there is still something to prove. You want to prove also that if two triangles have the same angle, then the quantity opposite side/hypothenuse is the same.

Where's the brainfart smiley when you need one?

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