Can this equation be solved? x+sin⁡(x)=11π48

Marquis Neal

Marquis Neal

Answered

2022-01-25

Can this equation be solved? x+sin(x)=11π48

Answer & Explanation

chaloideq1

chaloideq1

Expert

2022-01-26Added 11 answers

f(x)=x+sinx is monotonically increasing, and without bounds, so there will be exactly one solution.
y=11π48 is (relatively) small, so a first guess is obtained by setting sinxx to get x11π96. An improved value is obtained by including the next term of the sine series,
2x16x3yxy2+y396
This gives the numerical value x=0.3638613210103829 which is already close to the (more) exact value 0.363965532996313

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