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

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- Jun 14th 2011, 07:48 AM #1

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- Jun 14th 2011, 08:08 AM #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 $\displaystyle \cos(x)^2$ equal to $\displaystyle (\cos(x))^2$ (a lot of brackets, especially if you have lots of trig functions) or $\displaystyle \cos(x^2)$?

IMO there are only four trig identities you need to know

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

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

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

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

You can derive all your other identities from these

- Jun 14th 2011, 08:23 AM #3

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## 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.

- Jun 14th 2011, 08:51 AM #4

- Jun 15th 2011, 12:06 AM #5

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- Jun 15th 2011, 06:13 AM #6

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