Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Iteration help

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...

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}}

(edited 7 years ago)

OP

Original post by Zacken

x = \arcsin \sqrt{\frac{x}{4}}

Thanks - where did pi come from for the other formula?

(edited 7 years ago)

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

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

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

(edited 7 years ago)

OP

Thanks for the help. 🙂

Original post by Electrogeek

Thanks for the help. 🙂

No worries. :smile:

:smile:

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