# sinx composition question

• Apr 28th 2013, 11:03 AM
ameerulislam
sinx composition question
I'm kind of confused with these

is $sin^2x$ and $sinx^2$ the same?

if they are they both can be written as $(sinx)^2$ ?
• Apr 28th 2013, 11:15 AM
Plato
Re: sinx composition question
Quote:

Originally Posted by ameerulislam
I'm kind of confused with these
is $sin^2x$ and $sinx^2$ the same?
if they are they both can be written as $(sinx)^2$ ?

Absolutely not.

You should use () with the sine function.

$\sin^2(x)=\left(\sin(x)\right)^2\ne\sin(x^2)$
• Apr 28th 2013, 11:27 AM
ameerulislam
Re: sinx composition question
Quote:

Originally Posted by Plato
Absolutely not.

You should use () with the sine function.

$\sin^2(x)=\left(\sin(x)\right)^2\ne\sin(x^2)$

does the sine it self has any value? I mean sine is useless without x (which can be 0 or any other degrees). That makes me wonder is $sin^2$ or $sin^2x$ is even valid..
• Apr 28th 2013, 12:20 PM
HallsofIvy
Re: sinx composition question
They're not. Unfortunately, we cannot make every write mathematics correctly (I've tried!) so we have to guess what they really mean!

$sin^2(x)= (sin(x))^2$ but $sin(x^2)$ is different.

For example, if x= 1 then sin(x)= sin(1)= 0.84147, approximately, so that $sin^2(1)= (sin(1))^2= (0.84147)^2= 0.70807$ while [tex]sin(x^2)= sin(1)= 0.84147[tex].
• Apr 28th 2013, 12:36 PM
Plato
Re: sinx composition question
Quote:

Originally Posted by ameerulislam
does the sine it self has any value? I mean sine is useless without x (which can be 0 or any other degrees). That makes me wonder is $sin^2$ or $sin^2x$ is even valid..

I did warn you not to use $\sin$ by itself!
It is a function notation. As such, it must be written in function notation: $\sin(x)$.

It is quite often the case that the notation $f^n(x)$ is used in place of $\left(f(x)\right)^n$.

In several computer algebra systems, one must use $\left(\sin(x)\right)^2$ for they will not recognize $\sin^2(x)$.

But again, reread my post. I told to use () with the sine function.