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

[InvalidID]

$$y+siny=x$$

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

 

[eumyang]

$$y+siny=x$$

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.

 

[InvalidID]

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

 

[SteamKing]

The presence of sin y. Trig functions are transcendental and cannot be solved using algebraic methods alone.

 

[ModusPwnd]

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,
$$\sin{y} = x$$
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.

 

[rbj]

you can graph $x$ as a function of $y$ 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

$$y + a \sin(y) = x$$

but you can still solve it numerically, as long as $|a| \le 1$. there are places in the $y=f(x)$ function where the slope is infinite, but only on a single point. sort of like the real function $y = x^{1/3}$.

 

[Bacle2]

Have you tried to apply the explicit function theorem to see if a local solution for y is
possible?

 

[HallsofIvy]

$$y+siny=x$$

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.