Question

Explain the solutions shown in the graph of sin(y^3/x)=0.

(As seen in the picture below)

Answer 1

Curiosity

Answer 2

sine function is 0 at x = 0 and x = pi
The general solution is x = n(pi) where n is any integer: positive, 0, negative.
y^3/x = n(pi)
y^3 = n(pi) * x
y = (n(pi))^(1/3) * x^(1/3)

So it is a plot of the cuberoot of x multiplied by a constant and the constant takes on infinite numbers of values (n(pi))^(1/3) for integer n from -infinity to +infinity.

Answer 3

hmm

Answer 4

The odd spacing in-between what seems to be doodles is interesting. Thanks for explaining :)

Answer 5

Plot it at: https://www.desmos.com/calculator
And if you zoom out a get a bigger picture, you will see a series of cuberoot plots. Due to the corresponding negative "n", the graph will be a reflection about the x axis. The doodle like appearance is due to numerous number of cuberoot plots spaced so closely together.

Answer 6

ahh, zooming in helps :)

Answer 7

*in/out

Answer 8

interesting plot indeed!

Answer 9

thanks for your explanation.

Answer 10

you are welcome.

Answer 11

Thank you both for an interesting question n answer :)