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

1. Mar 13, 2013

### InvalidID

$$y+siny=x$$

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

2. Mar 13, 2013

### eumyang

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

3. Mar 13, 2013

### InvalidID

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

4. Mar 13, 2013

### SteamKing

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

5. Mar 13, 2013

### ModusPwnd

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.

6. Mar 13, 2013

### 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. sorta like the real function $y = x^{1/3}$.

7. Mar 13, 2013

### Bacle2

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

8. Mar 13, 2013

### HallsofIvy

Staff Emeritus
Graph y= x+ sin(x), then flip the x and y axes.