Find dy/dx if y= (x²-3)³cos2x
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Both refer to the inverse sine function.
The inverse sine (or arcsine) of x:
where x is a real number in the domain of the function:
and the arcsine function returns an angle in the interval![\mathsf{\left[-\,\frac{\pi}{2},\,\frac{\pi}{2}\right]:}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cleft%5B-%5C%2C%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%5C%2C%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cright%5D%3A%7D)
So if you see anywhere one of these expressions below
then you should look for an angle
that satisfies the following conditions:
This angle is called the inverse sine of the real number x.
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Pay attention and do not mistake the arcsine function for the reciprocal of sine (which is cosecant); especially if you prefer or see that notation with an superscript -1. This one can be easily mistaken for an exponent:
but the reciprocal is something like
![\mathsf{\big[sin(x)\big]^{-1}=\dfrac{1}{sin\,(x)}=csc(x)\qquad\quad(!!)}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cbig%5Bsin%28x%29%5Cbig%5D%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7Bsin%5C%2C%28x%29%7D%3Dcsc%28x%29%5Cqquad%5Cquad%28%21%21%29%7D)
and this last one has a total different meaning.
I hope this helps. =)
_______________
Both refer to the inverse sine function.
The inverse sine (or arcsine) of x:
where x is a real number in the domain of the function:
and the arcsine function returns an angle in the interval
So if you see anywhere one of these expressions below
then you should look for an angle
This angle
______
Pay attention and do not mistake the arcsine function for the reciprocal of sine (which is cosecant); especially if you prefer or see that notation with an superscript -1. This one can be easily mistaken for an exponent:
but the reciprocal is something like
and this last one has a total different meaning.
I hope this helps. =)