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Homework Help: Value of y

  1. Nov 30, 2009 #1
    http://img194.imageshack.us/img194/1383/68225760.png [Broken][/URL]

    sin-1x=y & siny=x
    tan-1x=y & tany=x

    The answer is E but I dont know how my teacher got to that. Can someone explain this to me please?
    1. The problem statement, all variables and given/known data
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 30, 2009 #2
    Do you understand the inverse trig functions? The inverse trig functions find the angle of the triangle that satisfies the given relation. That is sin-1(t) is the angle theta such that sin(theta)=t. If you view t as t/1, then can you set up a triangle that has this property? Can you then find the length of the remaining edges so that you can find tan(theta), i.e. tan(sin-1(t))?
  4. Nov 30, 2009 #3
    I'm still very confused
  5. Nov 30, 2009 #4
    Okay. Set θ=sin-1(t). This means that sin(θ)=t (i.e. sin(θ)=t/1). This means that in a right triangle with one angle that is θ, the side opposite θ has length t and the hypotenuse has length 1. You can find the side adjacent to θ by using the Pythagorean theorem. Then all you have to do is find tan(θ) since tan(θ)=tan(sin-1(t)).
  6. Nov 30, 2009 #5
    Okay, thank you so much you cleared that right up!
  7. Nov 30, 2009 #6
    No problem! That is the general technique when doing these type of trig problems that contain inverse trig functions.
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