1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Basic trigonometry

  1. Dec 25, 2012 #1
    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. jcsd
  3. Dec 25, 2012 #2


    User Avatar
    Science Advisor

    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.
  4. Dec 25, 2012 #3
    How can one prove that sin theta = opposite side / hypotenuse ?
  5. Dec 25, 2012 #4


    User Avatar
    Science Advisor

    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?
  6. Dec 25, 2012 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    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.
  7. Dec 25, 2012 #6


    User Avatar
    Science Advisor

    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

Similar Discussions: Basic trigonometry
  1. Trigonometry Question (Replies: 7)