Notation of Pythagorean identities are a bit confusing

[chromechris]

Say I have cos2(theta) . If I square such amount, I write it as cos^2(2(theta)), which seems like a non-intuitive way to write such. I would instead write such as cos(2(theta))^2 . I understand that that looks like the amounts in parentheses in theta are being squared, but maybe a different unique notation would work. I feel that cos^2(2(theta)) could be translated to a different amount say, 4^2(5*2) which equals 160. Instead if I wrote this same expression in the alternate notation that from Pythagorean identities that seems more intuitive I would write: (4(5*2))^2 which equals 1600. The notation causes me to yield different answers obviously. Just a random thought.

[Guest]

Say I have cos2(theta)

That's extremely ambiguous. i THINK you intend cos(2theta) which means "first multiply theta by 2 then
take the cosine function. Some people will write "x2" when they mean [tex]x^2[/tex]. That's ba d notation but it is done and it is better to avoid any possible misunderstanding.

If I square such amount, I write it as cos^2(2(theta)), which seems like a non-intuitive way to write such. I would instead write such as cos(2(theta))^2 . I understand that that looks like the amounts in parentheses in theta are being squared, but maybe a different unique notation would work.

I could understand it you wanted to write (cos(2(theta)))^2 but cos(2(theta))^2 is still ambiguous.

Do you understand the difference between "f" and "f(x)"? The first refers to the function f, the second to the numeric value of f evaluated at x. "f^2" means "the function f, squared". That's the standard notation and means that we are now working with a new function. If we call that new function "g" defined by g= f^2. And f(x) means "the function f applied to x" so, since g= f^2, g(x)= f^2(x). That is, by definition, the same as g(x)= (f(x))^2.