How to solve this trigonometric equation x=\frac{1}{2}\cos(\frac{2}{3}\sin(\frac{3}{4}x))+1 The iterative solution seems

Scoopedepalj

Scoopedepalj

Answered question

2022-02-26

How to solve this trigonometric equation x=12cos(23sin(34x))+1
The iterative solution seems to be 1.417.

Answer & Explanation

Kathryn Duggan

Kathryn Duggan

Beginner2022-02-27Added 7 answers

You can easily get extremely accurate approximations using (for example) Wims function calculator, by searching the root x of
f(x)=x[12cos(23sin(34x))+1]
(say between -5 and 5). Computing its value up to a mild number of digits gives
x=1.417520004
While Inverse symbolic calculator does not recognize this, it does lead to the approximation
x10sin(1)eexp(γ)=1.417520089
where γ is Euler's constant (=0.5772156649)

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