How Do I Know the Following Equations is Dimensionally Correct?

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The discussion revolves around determining the dimensional correctness of the equation y=2 cm * cos(k*x) with k=2 m^-1. The variables x and y are not explicitly defined in the problem, leading to confusion about their physical dimensions. It is suggested that y represents a displacement, while x could be an angle or arc length, as kx must yield a dimensionless quantity in radians. The relationship indicates that y's dimension should align with the output of the cosine function. Clarification on the definitions of x and y is essential for confirming the equation's dimensional accuracy.
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Homework Statement


The problem asks to choose the dimensionally correct equation. In the back of the book it says that the correct answer is y=2 cm * cos(k*x), where k=2 m^-1. What do x and y stand for? The book doesn't say. Does each variable usually represent a certain dimension in physics? From my understanding, dimension y should be the same as dimension ( 2 cm * cos(k*x) ). But what is y?


Homework Equations





The Attempt at a Solution

 
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If you had y=cosθ, cosθ is dimensionless but θ would be in radians. What should x be then?
 
Appears to be dealing with harmonics. Notably spring harmonics. If so 'y' would be vertical or horizontal displacement.
 
rock.freak667 said:
If you had y=cosθ, cosθ is dimensionless but θ would be in radians. What should x be then?

an angle? arc length?
 
JustSomeGuy80 said:
an angle? arc length?

kx should give radians if k is m-1, x would be?
 

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