Why is it impossible to solve y explicitly in this equation?

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  • #1
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$$y+siny=x$$

How would you even graph a function like this if you can't solve for y explicitly?
 

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  • #2
eumyang
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$$y+siny=x$$

How would you even graph a function like this if you can't solve for y explicitly?
Make a table of values. Pick some y-values and solve each of them for x.
 
  • #3
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Why is it impossible to solve y explicitly in this equation?
 
  • #4
SteamKing
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The presence of sin y. Trig functions are transcendental and cannot be solved using algebraic methods alone.
 
  • #5
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The presence of sin y. Trig functions are transcendental and cannot be solved using algebraic methods alone.
With this in mind (and I agree) one cannot solve this either,
[tex] \sin{y} = x [/tex]
We have to invent a special function, the inverse sine, to solve it. By that same logic, we can invent a special function to solve the original equation. But it would be no more "solved" than using the inverse sine function to solve my equation above.
 
  • #6
rbj
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you can graph [itex]x[/itex] as a function of [itex]y[/itex] explicitly, then turn the graph by 90° and flip (mirror image) the rotated graph.

i do not think there is a closed form solution to

[tex] y + a \sin(y) = x [/tex]

but you can still solve it numerically, as long as [itex] |a| \le 1 [/itex]. there are places in the [itex]y=f(x)[/itex] function where the slope is infinite, but only on a single point. sorta like the real function [itex] y = x^{1/3} [/itex].
 
  • #7
Bacle2
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Have you tried to apply the explicit function theorem to see if a local solution for y is
possible?
 
  • #8
HallsofIvy
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$$y+siny=x$$

How would you even graph a function like this if you can't solve for y explicitly?
Graph y= x+ sin(x), then flip the x and y axes.
 

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