1. Not finding help here? Sign up for a free 30min 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!

Tan(t) = x/a => sin(t) = x/sqrt( a^2 + x^2) ?

  1. Jul 13, 2008 #1
    tan(t) = x/a => sin(t) = x/sqrt( a^2 + x^2) ???

    Folks,

    In the solution guide to Kline's calculus book, he gives the following in working a problem:

    tan(t) = x/a => sin(t) = x/sqrt( a^2 + x^2)

    Can someone explain why this is the case?

    Thanks,

    Tristan
     
  2. jcsd
  3. Jul 13, 2008 #2

    rock.freak667

    User Avatar
    Homework Helper

    Re: tan(t) = x/a => sin(t) = x/sqrt( a^2 + x^2) ???

    tan(t)=Opposite/Adjacent. Draw a right-angled triangle with the side opposite to the angle ,t, as x and the adjacent side to it as a. Then use pythagoras' theorem.
     
  4. Jul 13, 2008 #3
    Re: tan(t) = x/a => sin(t) = x/sqrt( a^2 + x^2) ???

    I just figured this out on my own. For anyone who is curious:

    tan(t) = x/a means the opposite and adjacent legs of a right triangle with angle t, are x and a respectively. By the Pythagorean Therom, this implies that the hypotenuse is sqrt(a^2 + x^2). Since sin t = opp/hyp, sin t = x/sqrt( a^2 + x^2). QED
     
  5. Jul 16, 2008 #4

    Gib Z

    User Avatar
    Homework Helper

    Re: tan(t) = x/a => sin(t) = x/sqrt( a^2 + x^2) ???

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

Have something to add?



Similar Discussions: Tan(t) = x/a => sin(t) = x/sqrt( a^2 + x^2) ?
  1. Intergrate e^(t(x^2)) (Replies: 3)

Loading...