Does this pic makes sense? (Trigonometry)

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    Trigonometry
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Discussion Overview

The discussion revolves around the interpretation of a graph depicting the sine function, specifically addressing the placement of the value "1" on the y-axis in relation to the multiples of pi on the x-axis. Participants explore the implications of scaling and the significance of the axes in the context of trigonometric functions.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the graph's representation, noting that if pi is approximately 3.14, the placement of "1" seems disproportionate.
  • Another participant clarifies that the "1" on the y-axis represents a value of 1, while the x-axis represents multiples of pi.
  • Concerns are raised about the visual scaling of the graph, suggesting that the lengths of the axes do not need to be uniform and can be adjusted for clarity.
  • Some participants argue that comparing the numerical values on different axes is meaningless, as they represent different quantities (angles in radians vs. sine values).
  • There is a discussion about whether all plotted functions need to have physical significance, with some asserting that the relationship between numbers can be explored without physical context.
  • Others emphasize that the specific graph in question has physical significance and that the axes represent different types of measurements, which should not be disregarded.

Areas of Agreement / Disagreement

Participants express differing views on the importance of physical significance in graphing functions and the validity of comparing values across different axes. There is no consensus on whether the scaling of the axes should be uniform or if the graph's representation is appropriate.

Contextual Notes

Participants highlight the limitations of comparing values on different axes due to their distinct meanings and units, indicating that assumptions about scaling and representation may vary based on context.

Femme_physics
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Does this pic make sense? If pi is equal to 3.14, how come it seems drawn at where 1 supposed to be?

[PLAIN]http://img210.imageshack.us/img210/6190/sine.jpg
 
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The 1 is on the y-axis, where the value is... umm... 1. The multiples of pi are on the x-axis.
 
CRGreathouse said:
The 1 is on the y-axis, where the value is... umm... 1. The multiples of pi are on the x-axis.
I know, but if you look at it carefully you can see that the "1" on the y-axis is way longer than the pi on the "x-axis"...how does that make sense if pi is equal to 3.14?
 
You can scale a graph physically however you want. Your "ticks", as I call them, can be spaced out however you want, as long as it is uniform on the axis. For example, let's say instead of graphing y = sin(x), you graphed y = 10000sin(x). If you actually drew your graph so that the length along the x-axis from 0 to pi matched the y-axis as you want, your graph would be so tall as to lose all usefulness.

edit: I say they have to be uniform on the axis... but that's not entirely true but for your purposes they do.
 
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I think you're wrong, Peng.

Are you saying that the X-plane and the Y-plane are simply not symmetrically aligned in this case?
 
Dory said:
I think you're wrong, Peng.

Are you saying that the X-plane and the Y-plane are simply not symmetrically aligned in this case?

If you mean they are not similar in the length scale, obvious they are not. And there is no need for them to be. Like I said, if you plotted something like 1000sin(x), would it make sense to allocate the same lengths per tick for the x and y axis?
 
Dory the quantities on the x-axis are different to those on the y axis.The x-axis is giving angles in radians and the y-axis is giving the sines of those angles.They are two different things so how can you compare the numerical values of them?It's rather like me saying that four seconds is bigger than three metres.It's a meaningless comparison.
 
Ah...getting the hang of it. Thanks.
 
Dadface said:
Dory the quantities on the x-axis are different to those on the y axis.The x-axis is giving angles in radians and the y-axis is giving the sines of those angles.They are two different things so how can you compare the numerical values of them?It's rather like me saying that four seconds is bigger than three metres.It's a meaningless comparison.

We shouldn't be worrying ourselves about the units that correspond with the graph. We could just as well be plotting something hypothetically numerical that has no physical significance. Pengwuino has already answered the question appropriately.

Another example, if we plotted y=x it will only look like there is a 45o angle between the line and the x-axis if the unit lengths on the x and y-axis are spaced equally apart. If we had 1cm=1 on the x-axis but 1cm=10 on the y-axis then it will look like y=x/10 instead of y=x.
 
  • #10
Mentallic said:
We shouldn't be worrying ourselves about the units that correspond with the graph. We could just as well be plotting something hypothetically numerical that has no physical significance. Pengwuino has already answered the question appropriately.

Another example, if we plotted y=x it will only look like there is a 45o angle between the line and the x-axis if the unit lengths on the x and y-axis are spaced equally apart. If we had 1cm=1 on the x-axis but 1cm=10 on the y-axis then it will look like y=x/10 instead of y=x.

Yes of course you can choose any scale you wish but also it is meaningless to make numerical comparisons between quantities that are different.The graph in question is physically significant,both quantities are unitless but they are different things.
 
  • #11
So you're saying that every function we plot needs to have some physical significance? We can't just find the relationship between two numbers by plotting an input and its appropriate output defined by some function?
 
  • #12
No I wasn't referring to "every function" I was referring to the function introduced by the op which is physically significant.
 
  • #13
Right, so if I showed you a quadratic then you would agree that the numbers can just be a relationship between each other. If I then changed my story around and told you this quadratic describes the motion of a projectile then everything suddenly changes? No, it has no reason to.

We are describing the relationship between the quantities on the x and y-axis as nothing more than numerical values. No matter what the units are, we are only comparing the relationship of the numbers. This isn't the reason why we change the scale of each axis, pengwuino has given the correct answer.
 
  • #14
You "are only comparing the relationship of the numbers"? .It is not valid to change the original question and consider the numbers only and ignore what those numbers stand for?The answers we give here should refer to the graph that has been presented which has one set of numbers referring to angles and the second set referring to sines of those angles,two different things.
 
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