How Do I Know the Following Equations is Dimensionally Correct?

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SUMMARY

The discussion centers on determining the dimensional correctness of the equation y = 2 cm * cos(k*x), where k = 2 m^-1. The variable y represents a physical dimension, likely vertical or horizontal displacement, while x is questioned as either an angle or arc length. The cosine function is dimensionless, indicating that the argument k*x must also be dimensionless, confirming that k must have units of m^-1. This leads to the conclusion that x must be in meters to maintain dimensional consistency.

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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?


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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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