#Negative exponent on sine
vital oreBOT
unborn turtle
sin^-1(x) is usually reserved for arcsin, the inverse of sin
but otherwise the exponent laws youre applying are fine
(sin(x))^(-1)=cosec(x)
bright dune
So I can’t do what I did if it involves sin, cos or tan
unborn turtle
youre better off writing 1/sin or something like that, or people can easily get confused
any other exponent is fine
bright dune
Thank you
But is there a way to express sin(x) to the power of -1?
Or is that not a thing
orchid flicker
1/cscx ?
unborn turtle
cosec(x)=1/sin(x)
orchid flicker
= 1/1/sinx = sinx
unborn turtle
wifi being slow as hell
bright dune
Oh the secants are above my level 😢
unborn turtle
the trig functions all have reciprocals
cosec=1/sin sec=1/cos cot=1/tan
thats the only way to write it unless you specify like (sin(x))^(-1)
bright dune
Can you use the chain rule for the derivative of those
unborn turtle
np
indigo geyser
But is there a way to express sin(x) to the power of -1?
If you write $(\sin x)^{-1}$, I think the reader will know you mean $\frac{1}{\sin x}$. But your question is very fair. The notation is very confusing.
worn leafBOT
SWR
indigo geyser
I think the difference here, in mathematical language, is the $\sin$ is a known to be a function. That means that $\sin^{-1}$ is understood to be the $\textit{inverse of a function}$, and NOT the reciprocal. Whereas $(\sin x)$ is known to be a number, so $(\sin x)^{-1}$ is known the be the reciprocal of that number. The same rule should apply for any function. A math student should know the difference between $f^{-1}(x)$ and $(f(x))^{-1}$
worn leafBOT
SWR
indigo geyser
But I've read a few math books that have argued against using $f^{-1}$ for this exact reason, but a better notation has not been adopted yet.
worn leafBOT
SWR
indigo geyser
bright dune
In my country it is common to use f and then in subscript “inv” for an inverse function
unborn turtle
ive never seen that one before
subtle lance
I think the difference here, in mathematical language, is the $\sin$ is a known ...
I can't believe you wrote sin instead of sine #1207418171204833311 message
uncut tide
I solved the problem for me. What do sin(x)^2, sin(x)^-1, sin(x^2), and asin(x) all mean? If you know what each one means, problem solved.
Never write sin^-1(x), and never write sin^2(x). Is sin^2(x) the square of the sine of x, or is it the sine of the sine of x? Is sin^-1(x) the reciprocal of the sine of x, or is it the arcsine of x? I don't know, and I don't care. The problem "What's 6/2*3?" can also go in the grave. No notation in this message is clear, and never use it.
gloomy wedge
.close