# Basic trigonometry

1. Dec 25, 2012

### iknownth

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?

2. Dec 25, 2012

### pwsnafu

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.

3. Dec 25, 2012

### iknownth

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

4. Dec 25, 2012

### pwsnafu

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?

5. Dec 25, 2012

### micromass

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.

6. Dec 25, 2012

### pwsnafu

Arrgh yes of course.

Where's the brainfart smiley when you need one?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook