1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Trigonometric Inverse

  1. Jul 27, 2011 #1
    1. The problem statement, all variables and given/known data
    I understand that y = sin -1 x. However, why is it that when one writes x = sin y, one leaves out the -1

    2. Relevant equations

    3. The attempt at a solution
    I know that when you invert a trig function, the dependent variable essentially switches from y to x and the independent variable switches from x to y. However, why do you leave out the -1 when you write the inverse sin as x = sin y ?
  2. jcsd
  3. Jul 27, 2011 #2


    User Avatar
    Homework Helper

    not sure if I understand the question, but if you start from
    [tex] y = sin^{-1} x [/tex]

    take the sin of both sides
    [tex] sin(y) = sin(sin^{-1} x) = x [/tex]
  4. Jul 27, 2011 #3
    I'm sorry I wasn't very clear. That answers my question though! I had no idea you could take the sin of the sin-1(x) and it would cancel them out. Thank you! :smile:
  5. Jul 27, 2011 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Well, that is how inverse functions work.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook