How Do I Know the Following Equations is Dimensionally Correct?

[JustSomeGuy80]

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

 

[rock.freak667]

If you had y=cosθ, cosθ is dimensionless but θ would be in radians. What should x be then?

 

[djeitnstine]

Appears to be dealing with harmonics. Notably spring harmonics. If so 'y' would be vertical or horizontal displacement.

 

[JustSomeGuy80]

If you had y=cosθ, cosθ is dimensionless but θ would be in radians. What should x be then?

an angle? arc length?

 

[rock.freak667]

an angle? arc length?

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