How do I simplify this?
tan(arcsin(x))
I have to know how to solve these problems by tomorrow morning and I'm dying here! Any help is appreciated.
i'll start you off. Let $\displaystyle \theta = \sin^{-1} x$
$\displaystyle \Rightarrow \sin \theta = x$
so we can draw a right triangle with an acute angle $\displaystyle \theta$ where the opposite side is $\displaystyle x$ and the hypotenuse is 1. by Pythagoras, the adjacent side will be $\displaystyle \sqrt{1 - x^2}$
so now, $\displaystyle \tan \left( \sin^{-1} x \right) = \tan \theta = ... $?
ok, so i almost did the entire problem...don't complain, i left the punch line for you
tan(arcsin(x))
let arcsin x =y then sin y =x, cos y =+[1-(sin y)^2]^(1/2) as we give
arcsin x a domain of [-pi/2, pi/2]
tan (arcsinx)= [sin (arcsin x)]/ [cos (arcsin x)]= x/(1-x^2)^(1/2)
sin (arcsinx)= x
should be correct, but if it is wrong
work in similiar manner
pretty much, there may be cases where things have to be treated differently. but definitely for any problem you will get of this type this will work. there are also ways to do them using formulas, and then there's calculus_jy's way.
really? i wasn't trying to explain it simple. you're just smart that's what it is. i've explained this even simpler with the aids of diagrams on this forum before. and there are other methods for doing them posted as well. do a search.Wow, I've never seen it explained so simply before.
you're welcomeThanks for this.yes it is!This site is greatlooking forward to your inputI'll be posting here a lot more often methinks. (I can help too, not just looking for homework answers)
that's correct...i suppose you were trying to type $\displaystyle \frac x{\sqrt{1 - x^2}}$
see our LaTeX Forum to learn how to use LaTeX. start at the tutorial (it is a sticky thread, so it will be the first thread in the list). there is a pdf file in the first post that gives you the codes