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

In summary, The y-axis on a sine graph represents the amplitude of the sine wave, which can be thought of as the y-coordinate on a unit circle when the radius makes an angle theta with the positive x-axis. When we type "sin(pi)" we get 0, which corresponds to the distance of a point on the unit circle from the x-axis. However, the scale on the y-axis is typically exaggerated for aesthetic purposes, so the length from 0 to 1 on the y-axis is actually larger than the length of 0 to 1 on the x-axis. This exaggeration can affect certain calculations, such as the slope of the tangent line to the graph. It is a common artistic technique to exaggerate scales for
  • #1
PhotonW/mass
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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?
 
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  • #2
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.
 
  • #3
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.
 
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  • #4
PhotonW/mass said:
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.
 
  • #5
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!)
 

What is the y axis for the sine wave?

The y axis for a sine wave represents the amplitude or height of the wave. It shows the maximum displacement of the wave from its equilibrium position.

Why is the y axis important in a sine wave?

The y axis is important in a sine wave because it allows us to visualize the amplitude of the wave, which is a crucial aspect of understanding the properties and behavior of the wave.

How is the y axis related to the x axis in a sine wave?

The y axis and the x axis in a sine wave are perpendicular to each other and together they form a coordinate system. The x axis represents time or distance, while the y axis represents the amplitude of the wave at a specific point in time or distance.

Can the y axis be negative in a sine wave?

Yes, the y axis can be negative in a sine wave. This occurs when the wave is in the negative or downward direction, indicating a negative amplitude or displacement from the equilibrium position.

How does the y axis change with different frequencies in a sine wave?

The y axis remains constant in a sine wave regardless of the frequency. However, the frequency of the wave affects the number of cycles or repetitions of the wave per unit time, which can change the shape of the wave on the y axis.

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