Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trigonometric Equations

  1. Apr 3, 2015 #1
    Is there any way I can reduce or simplify expressions like cos(sin-1(x)), sin(cos-1(x)), cos(tan-1(x)), tan(cot-1(x)) etc.? (I refer to the arc functions, i.e. inverses, by the superscript -1, not the reciprocals)
     
  2. jcsd
  3. Apr 3, 2015 #2

    Svein

    User Avatar
    Science Advisor

    Hint: sin(sin-1(x)) = x and cos(w) = sin(w+π/2).
     
  4. Apr 3, 2015 #3
    You can use this relation:
    ArcSin((1-x^2)^0.5)=ArcCos(x)
     
  5. Apr 3, 2015 #4

    Mentallic

    User Avatar
    Homework Helper

    Draw a right triangle with an angle [itex]\theta[/itex], opposite side length of x and hypotenuse length 1. Now from this triangle, by definition,

    [tex]\sin\theta = x[/tex]
    hence
    [tex]\theta = \sin^{-1}x[/tex]

    So then what is [itex]\cos\left(\sin^{-1}x\right)[/itex], or more simply, [itex]\cos\theta[/itex] ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trigonometric Equations
  1. Trigonometric equation (Replies: 2)

Loading...