- #1

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## Main Question or Discussion Point

$$y+siny=x$$

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

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

- Thread starter InvalidID
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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?

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

- #2

eumyang

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Make a table of values. Pick some y-values and solve each of them for x.$$y+siny=x$$

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

- #3

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

- #4

SteamKing

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- #5

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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

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i do not think there is a

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

but you can still solve it numerically, as long as [itex] |a| \le 1 [/itex]. there

- #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?

possible?

- #8

HallsofIvy

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Graph y= x+ sin(x), then flip the x and y axes.$$y+siny=x$$

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

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