# Basic trigonometry

by iknownth
Tags: trigonometry
 P: 16 We all know that 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?
P: 839
 Quote by iknownth But why? Are there some explanations behind or are they just defined by scientists?
What do you mean by "explanations"?

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.
 P: 16 How can one prove that sin theta = opposite side / hypotenuse ?
P: 839
Basic trigonometry

 Quote by iknownth How can one prove that sin theta = opposite side / hypotenuse ?
I'm assuming planar geometry here. There are two answers:
1. It is the definition of sine. There is nothing to prove.
2. 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 your definition of sine?
Mentor
P: 18,346
 Quote by pwsnafu It is the definition of sine. There is nothing to prove.
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.