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Which value to choose from the solutions of transcendental equation?

Hi, I want to find the solution of a transcendental equation. I got three solutions to the equation. Typically, the solution for 'b' are either greater than Pi or less than Pi [including the value at Pi]. Please suggest that whether the value greater than or less than to be taken. Using MATHEMATICA: f = Pi - b - 1.2*Sin[b]; Rts = Reduce[f == 0, b, Reals] * Solution for Pi = b + XSin[b] b == 2.11485 || b == 3.14159 || b == 4.16833.

4 Replies
Posted 9 years ago

Mathematically, these three roots are equally valid. If there is a reason to prefer one over the other two, it must come from some understanding of the of the meaning behind the mathematics. For example, in problems which have solutions from quadratic forms, it is frequently the case that there is a negative solution with no valid physical meaning, and it is discarded.

In[1]:= NSolve[Pi - x - 1.2*Sin[x] == 0, x, Reals, 15]

Out[1]= {{x -> 2.11485436221882}, {x -> 3.14159265358979}, {x -> 
   4.16833094496076}}

In[2]:= Plot[Pi - x - 1.2*Sin[x], {x, 0, 2 Pi}]

enter image description here

POSTED BY: David Keith

Hi, Simpson and Cardin, thanks for your help. But the difficulty is if you go through my post , I got the same soutions as you have obtained. The point is for a particular value of X [here X = 1.2], three solutions are there. Now, which of the two roots [excluding the root at b = Pi] are to be considered and why.

NSolve[Pi - x - 1.2*Sin[x] == 0, x, Reals, 15]

{{x -> 2.11485436221882}, {x -> 3.14159265358979}, {x -> 4.16833094496076}}

POSTED BY: Simon Cadrin
Posted 9 years ago

.

Plot[Pi - b - 1.2*Sin[b], {b, 0, 5}]
POSTED BY: Bill Simpson
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