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Math Help - trigonometry Addition Formulae (v)

  1. #1
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    trigonometry Addition Formulae (v)



    The diagram shows a kite whose leading diagonal forms the diameter of a circle. Find the exact value of sin XOY

    What I want to know is, do I need to find the diameter, if so, how?
    Last edited by r_maths; January 7th 2007 at 07:42 AM.
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  2. #2
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    Quote Originally Posted by r_maths View Post


    The diagram shows a kite whose leading diagonal forms the diameter of a circle. Find the exact value of sin XOY

    What I want to know is, do I need to find the diameter, if so, how?
    That means the inscribed angle X0Y is 90 degree.
    Thus, sin 90 = 1
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    That means the inscribed angle X0Y is 90 degree.
    Thus, sin 90 = 1
    my bad, the sides are not equal so you cant 360/4.
    root 5 & 3 are the length of the sides of the kite

    the answer is 3 root5 / 7
    i dont know how to arrive at that.
    (just to let you know, no calculator allowed)
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  4. #4
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    Hello, r_maths!

    The diagram shows a kite whose leading diagonal forms the diameter of a circle.
    Find the exact value of \sin(XOY).

    Look at half of the kite . . .
    Code:
          Z
          *
          | *   _
          |   *√5
          |     *
       __ |   90 * Y
      √14 |      *
          |     *
          |    *
          |   * 3
          |θ *
          | *
          |*
          *
          O

    Since ZO is a diameter, \angle Y = 90^o.

    Using Pythagorus, we find that: . ZO = \sqrt{14}


    Let \theta = \angle ZOY
    Then: . \sin\theta = \frac{\sqrt{5}}{\sqrt{14}},\;\cos\theta = \frac{3}{\sqrt{14}}

    Then: . \sin(XOY) \:=\:\sin(2\theta) \:=\:2\sin\theta\cos\theta \:=\:2\left(\frac{\sqrt{5}}{\sqrt{14}}\right)\left  (\frac{3}{\sqrt{14}}\right) \:=\:\frac{3\sqrt{5}}{7}

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  5. #5
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    Quote Originally Posted by Soroban View Post
    Hello, r_maths!


    Look at half of the kite . . .
    Code:
          Z
          *
          | *   _
          |   *√5
          |     *
       __ |   90 * Y
      √14 |      *
          |     *
          |    *
          |   * 3
          |θ *
          | *
          |*
          *
          O

    Since ZO is a diameter, \angle Y = 90^o.
    how did you work out that angle was 90 ?
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