Multiplication with modulus of function

[Silva_physics]

Hi!
Could anybody, please, tell me:
whether |Cos(theta)|*Cos(theta) = Cos^(theta) , because it means that only positive values of Cos(theta) are taken.
Am I right?:shy:

 

[Silva_physics]

= Cos^2(theta)

 

[HallsofIvy]

Hi!
Could anybody, please, tell me:
whether |Cos(theta)|*Cos(theta) = Cos^(theta) , because it means that only positive values of Cos(theta) are taken.
Am I right?:shy:

That's not a well phrased question. |Cos(theta)| is necessarily positive but the "Cos(theta)" outside the "modulus" is not so resticted.

In general |a|*a is equal to $a^2$ if a is non-negative, but equal to $-a^2$ if a is negative.

 

[Silva_physics]

Thanks

 

[CellCoree]

Hello! That's a great question. The answer is yes, you are correct. When you multiply a function by its modulus, you are essentially taking the absolute value of that function. In the case of cos(theta), this means that only positive values of cos(theta) will be used in the multiplication. So, the result of |cos(theta)|*cos(theta) will be equivalent to cos^2(theta), as you mentioned. This can be seen graphically by looking at the graph of cos(theta), which only has positive values. I hope this helps clarify things for you!