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Thread: sinx composition question

  1. #1
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    sinx composition question

    I'm kind of confused with these

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

    if they are they both can be written as $\displaystyle (sinx)^2$ ?
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  2. #2
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    Re: sinx composition question

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

    Absolutely not.

    You should use () with the sine function.

    $\displaystyle \sin^2(x)=\left(\sin(x)\right)^2\ne\sin(x^2)$
    Thanks from ameerulislam
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  3. #3
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    Re: sinx composition question

    Quote Originally Posted by Plato View Post
    Absolutely not.

    You should use () with the sine function.

    $\displaystyle \sin^2(x)=\left(\sin(x)\right)^2\ne\sin(x^2)$
    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 $\displaystyle sin^2$ or $\displaystyle sin^2x$ is even valid..
    Last edited by ameerulislam; Apr 28th 2013 at 11:52 AM.
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  4. #4
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    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!

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

    For example, if x= 1 then sin(x)= sin(1)= 0.84147, approximately, so that $\displaystyle sin^2(1)= (sin(1))^2= (0.84147)^2= 0.70807$ while [tex]sin(x^2)= sin(1)= 0.84147[tex].
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  5. #5
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    Re: sinx composition question

    Quote Originally Posted by ameerulislam View Post
    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 $\displaystyle sin^2$ or $\displaystyle sin^2x$ is even valid..
    I did warn you not to use $\displaystyle \sin$ by itself!
    It is a function notation. As such, it must be written in function notation: $\displaystyle \sin(x)$.

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

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

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