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Trigonometric Identity: Double Angle.

  1. May 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Here is the question given:

    A blade for a lawnmower consists of two parts made of the same material and joined together as shown:

    Untitled.jpg

    The length OP is one unit in length and MPQN is square in shape.

    Develop an equation for the cross-sectional area of the blade and find the magnitude of angle ∅ to give the area of the blade.

    2. Relevant equations

    sin 2 ∅ = 2 ((sin ∅) (cos ∅)

    3. The attempt at a solution

    Attempt? I've tried deriving the double angle equation but cant get anywhere... :( basically there is only one known piece of info (in the hypotenuse being one unit in length)...
     
    Last edited: May 5, 2012
  2. jcsd
  3. May 5, 2012 #2

    LCKurtz

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    I guess you mean express the area of the blade in terms of ##\phi##. Use trig to express PM and OM in terms of ##\phi##, then use that to calculate the two areas.
     
  4. May 5, 2012 #3
    I know what you mean and thank you.

    But what I dont know is what to do from there to get some physical/actual answer...
     
  5. May 5, 2012 #4

    LCKurtz

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    Well, I don't know what else to do either because the statement "find the magnitude of angle ∅ to give the area of the blade" doesn't mean anything to me.
     
  6. May 5, 2012 #5
    I think it simply means find the value of theta, and in turn, use that value to find the surface area of the blade.
     
  7. May 5, 2012 #6

    LCKurtz

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    But there isn't "a value of ##\phi##". As ##\phi## varies so does the area. You can express the area in terms of ##\phi##. I think the rest of the problem isn't properly stated.
     
  8. May 5, 2012 #7
    I know and this is what confuses me. You can express the area in terms of ##\phi## yes, but this wont get me anywhere. I have written the question essentially the same, so maybe there is an error with the question.
     
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