1. ## cos(x) * cos(x)

Why is it that cos(x) * cos(x) = cos^2(x) as opposed to cos(x)^2 ?

Is this something to do with the trig identities? What identities are useful to know off by heart?

Thanks

2. ## Re: cos(x) * cos(x)

It's a convention and, as will all conventions, it eliminates ambiguity. Nothing to do with identities, they still hold.

Is $\cos(x)^2$ equal to $(\cos(x))^2$ (a lot of brackets, especially if you have lots of trig functions) or $\cos(x^2)$?

IMO there are only four trig identities you need to know

$\sin^2(x) + \cos^2(x) = 1$

$\sin (A \pm B) = \sin(A)\cos(B) \pm \cos(A)\sin(B)$

$\cos(A \pm B) = \cos(A)\cos(B) \mp \sin(A)\sin(B)$

$\tan(x) = \dfrac{\sin(x)}{\cos(x)}$

You can derive all your other identities from these

3. ## Re: cos(x) * cos(x)

Although it is not a good notation, many people don't write the ( ) in sin(x), just sin x. That would make it too easy to confuse (sin(x))^2 with sin(x^2). Of course, you can write (sin(x))^2 (with the parentheses) but it is simpler to write sin^2(x). In general, if f(x) is a function of x, f^2(x) means f(x)*f(x)= (f(x))^2.

4. ## Re: cos(x) * cos(x)

Originally Posted by Consumariat
Why is it that cos(x) * cos(x) = cos^2(x) as opposed to cos(x)^2 ?
FYI: Almost all computer algebra systems require it be written as $\cos(x)^2$.
That took me for ever to do it that way.

5. ## Re: cos(x) * cos(x)

oooooooooo!!!!!!!!!!
Thanks for that. I could never do cos^2 x on my calculator. Now i know how to do it

6. ## Re: cos(x) * cos(x)

Cheers for all the input. It's all a bit clearer now.