How do you solve the trigonometric equation sin ⁡ ( x ) + x = 9?How do you solve the trigonometric equation sin ⁡ ( x ) + x = 9? More generally, how do you solve equations with both trigs and 'x's without graphing? And maybe I only want real number answers.Suggestions and edit: If you use the Taylor Series, you will basically end up with at least 6 t h degree equations, if you want to make it close. Equation Solvers Are NOT Allowed. That will kind of limit you to this:(assuming you make careless mistakes, just like me, so you don't want cubic equations) x + x = 9.This yields x = 4.5, which is DEFINITELY a bad estimation.Thanks for helping me! It's just that I don't know what Newton-Ralphson and iterations are. Can you explain it to me or give me a link?

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How do you solve the trigonometric equation   sin  ⁡  (  x  )  +  x  =  9?How do you solve the trigonometric equation   sin  ⁡  (  x  )  +  x  =  9? More generally, how do you solve equations with both trigs and &#039;x&#039;s without graphing? And maybe I only want real number answers.Suggestions and edit: If you use the Taylor Series, you will basically end up with at least       6          t      h       degree equations, if you want to make it close. Equation Solvers Are NOT Allowed. That will kind of limit you to this:(assuming you make careless mistakes, just like me, so you don&#039;t want cubic equations)  x  +  x  =  9.This yields   x  =  4.5, which is DEFINITELY a bad estimation.Thanks for helping me! It&#039;s just that I don&#039;t know what Newton-Ralphson and iterations are. Can you explain it to me or give me a link?

h2a2l1i2morz · Accepted Answer

The function   sin  ⁡  x  +  x  −  9 has the strictly non-negative derivative   cos  ⁡  x  +  1, so the solution in       R   is unique, confined to   [  8  ,    10  ]. The Newton-Raphson method   x  ↦  x  −            sin      ⁡      x      +      x      −      9              cos      ⁡      x      +      1       iteratively improves the estimate       x    0    =  8 to   8.0125448260685 (according to my Python), if that&#039;s accurate enough.

How do you solve the trigonometric equation sin(x)+x=9?

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