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    Hello everyone,

    I have been given the formula

    X - 4 sin^2 (x) = 0

    I know that there's a root between 2 and 2.5 due to change in sign, but I can't find the suitable iterative formula.

    Can someone help me find the iterative formula - I thought that it might be x = 4 sin^2 (x), but this doesn't seem to work...
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    (Original post by Electrogeek)
    Hello everyone,

    I have been given the formula

    X - 4 sin^2 (x) = 0

    I know that there's a root between 2 and 2.5 due to change in sign, but I can't find the suitable iterative formula.

    Can someone help me find the iterative formula - I thought that it might be x = 4 sin^2 (x), but this doesn't seem to work...
    x = \pi - \arcsin \sqrt{\frac{x}{4}}
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    (Original post by Zacken)
    x = \arcsin \sqrt{\frac{x}{4}}
    Thanks - where did pi come from for the other formula?
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    (Original post by Electrogeek)
    That gives me the answer for the other root (0.26 radians) - I can't find it between 2 and 2.5 - thanks for the help though.
    see my edited answer
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    (Original post by Electrogeek)
    Thanks - where did pi come from for the other formula?
    Re-arrange the equation to \sin x = \sqrt{\frac{x}{4}}, then you know that x = \arcsin\sqrt{\frac{x}{4}} or x = \pi - \arcsin \sqrt{\frac{x}{4}} (mod 2pi)

    because \sin x = k \iff \sin(\pi-x) = k or by using a cast diagram
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    (Original post by Electrogeek)
    Thanks - where did pi come from for the other formula?
    Note \sin(\pi-x)=\sin(x) for all x, using the \sin(A+B) rule.

    Then you can find the iterative formula for x-4 \sin^2 (\pi-x)=0.

    Edit: I would have first tried a Newton Raphson method for this equation though
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    Thanks for the help. 🙂
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    (Original post by Electrogeek)
    Thanks for the help. 🙂
    No worries.
 
 
 
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