What is the meaning of the y-axis on a sine wave graph?

[PhotonW/mass]

Okay this has been bothering me, I know what the x-axis on sine graph mean, but not the y axis. I know when I type for example: sin(pi) I will get 1. But what is that 1? I know its the y cordnate. But what is it?

 

[SteamKing]

It's the amplitude of the sine wave.

Since the sine function is related to a unit circle, think of the amplitude as the y coordinate on the unit circle when the radius makes an angle theta to the positive x-axis.

 

[Ferramentarius]

Sine(pi) equals zero. Geometrically the sine of angle α equals the length of the opposite side divided by the length of the hypotenuse in a right triangle. The particular size of the triangle is unrelevant as long as it contains the angle. In an unit circle centered at the origin sine(α) equals the distance of a point on the circumference (at angle α) from the x-axis. It corresponds to the imaginary part of e^(iα) in complex analysis.

 

[HallsofIvy]

Okay this has been bothering me, I know what the x-axis on sine graph mean, but not the y axis. I know when I type for example: sin(pi) I will get 1. But what is that 1? I know its the y cordnate. But what is it?

I am wondering what you think the x-axis "means" and what kind meaning you want the y-axis to have. The only "meaning" the x-axis in any graph has is the values of x, the independent variable. And the only "meaning" the y-axis has is the value of y the function assigns to the corresponding x.

And, by the way, "sin(pi)" is 0, not 1.

 

[Stephen Tashi]

In plotting the function sin(x) where x is in radians, the scale of on the y-axis is traditionally larger than the scale on the x-axis to make the picture look nicer (more "wavy"). So the length from 0 to 1 on the y-axis is longer than the length of 0 to 1 on the x axis. If you wanted to draw an "honest" graph, you would make a length of 1 on the y-axis equal to whatever length you chose for 1 radian on the x-axis.

On an exaggerated graph, if you try to measure the slope of the tangent line to the graph of sin(x) in terms of the angle it makes with the x-axis, you'll get the wrong answer since you won't be using the same scale in both the vertical and horizontal directions. (This line of thinking also shows why the derivative of the function sin(x) where x is in degrees is a different than derivative of sin(x) where x is in radians.)

Exaggeration of vertical scales for an artistic effect is common. For example in most "realistic" computer renderings of terrain ( on Earth or on other planets) the vertical scale in the picture is exaggerated. As another example, books for artists teach that the human figure is "7 heads" tall, but statistically this is an exaggeration. (People who draw fashion drawings for clothing advertisements are taught to draw figures that are 8 or 9 heads tall!)