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!

Is arcsin sin rotated by 90°?

  1. Jun 25, 2010 #1

    zxh

    User Avatar

    Sry, noob, but i didn't find this anywhere.
     
  2. jcsd
  3. Jun 25, 2010 #2
    No. Try Google.
     
  4. Jun 25, 2010 #3

    Mark44

    Staff: Mentor

    The two functions are inverses of one another. In general, the graphs of y = f(x) and x = f-1(y) are identical, but the graphs of y = f(x) and y = f-1(x) are reflections of each other in the line y = x.

    The situation is a little more complicated with y = sin(x) and y = arcsin(x) = sin-1(x) since the graph of the sine function isn't one-to-one (making the inverse not a function). The usual way around this is to restrict the domain of the sine function, defining y = Sin(x) = sin(x), with x restricted to the interval -pi/2 <= x <= pi/2.
     
  5. Jun 25, 2010 #4

    zxh

    User Avatar

    So the title would be true for -sin, viewed as a curve?
     
  6. Jun 25, 2010 #5

    Mark44

    Staff: Mentor

    Are you asking whether y = arcsin(x) is the rotation by 90 deg of y = -sin(x)? If that's the question, then no.

    If that isn't the question, then what are you asking?
     
  7. Jun 25, 2010 #6
    No it's only a segment of the curve, but the graph of y=arcsin(x) would fit over y=-sin(x) if rotated 90° either way about the origin.
     
    Last edited: Jun 25, 2010
  8. Jun 25, 2010 #7

    zxh

    User Avatar

    Thanks, that's what i was looking for. I'm not too concerned about range definitions.
    I came to this looking for a trig definition of a (half) circle (not the pythagorean Sqrt(r-x^2)).
    At first i was wondering why Cos(Sin(x)) (given that the 2 functions for a circle in a parametric plot are sinx and cosx) didn't work but it turns out it's
    Cos(ArcSin(x)).
     
  9. Jun 25, 2010 #8

    disregardthat

    User Avatar
    Science Advisor

    You can show this algebraically. If you are familiar with complex numbers, this is easy.
    1) multiply x+i (-sin x) with e^(i*pi/2) to rotate it by 90 degrees.
    2) reflect x+i(-sin x) over the curve y=x to invert it.
     
  10. Jun 25, 2010 #9

    zxh

    User Avatar

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




Similar Discussions: Is arcsin sin rotated by 90°?
  1. Sin(90) problem (Replies: 1)

  2. Sin 90 + theta (Replies: 14)

  3. Arccos and arcsin (Replies: 4)

Loading...