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# Iteration help

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1. 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...
2. (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...
3. (Original post by Zacken)
Thanks - where did pi come from for the other formula?
4. (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.
5. (Original post by Electrogeek)
Thanks - where did pi come from for the other formula?
Re-arrange the equation to , then you know that or (mod 2pi)

because or by using a cast diagram
6. (Original post by Electrogeek)
Thanks - where did pi come from for the other formula?
Note for all , using the rule.

Then you can find the iterative formula for .

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

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