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安裝中文字典英文字典辭典工具!
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- Proof for the formula of sum of arcsine functions $ \\arcsin x . . .
It is known that \\begin{align} \\arcsin x + \\arcsin y =\\begin{cases} \\arcsin( x\\sqrt{1-y^2} + y\\sqrt{1-x^2}) \\\\\\quad\\text{if } x^2+y^2 \\le 1 amp;\\text{or
- trigonometry - Why is $\arcsin(\sin(x))$ equal to $x$? - Mathematics . . .
By definition, $\arcsin\colon[-1,1]\longrightarrow\left[-\frac\pi2,\frac\pi2\right]$ is the inverse of the restriction to $\left[-\frac\pi2,\frac\pi2\right]$ of the
- Maclaurin expansion of $\\arcsin x$ - Mathematics Stack Exchange
I'm trying to find the first five terms of the Maclaurin expansion of $\arcsin x$, possibly using the fact that $$\arcsin x = \int_0^x \frac{dt}{(1-t^2)^{1 2}} $$ I can only see that I can interchange differentiation and integration but not sure how to go about this Thanks!
- trigonometry - What is the alternate form of $\,\arcsin x . . .
$\sin x$ can be expressed as $$\frac{e^{ix} - e^{-ix}}{2i}$$ through transformations using Euler's formula I am wondering if $\arcsin x$ has an equivalent, perhaps in logarithms
- analysis - Learning $\arcsin, \arccos, \arctan$ - how to? - Mathematics . . .
When you have $\arcsin (\sin(x))$ you may be shifted by factors of $\pi$ Finally when you have $\sin(\arccos(\frac 13))$ draw a right triangle with $\cos$ of one angle $\frac 13$ , so it is a $1-\sqrt 8-3$ triangle and find the sine of the angle, here $\frac 13\sqrt 8$
- functions - How to calc arc sine without a calculator? - Mathematics . . .
That first one sure converges slowly for values near 1, though – e g to do arcsin 0 999 to 20 decimal places takes 40,000 terms! It seems that how to use the second method was left as an exercise to the reader so I'll keep trying to make sense of it $\endgroup$ –
- trigonometry - Etymology of $\arccos$, $\arcsin$ $\arctan . . .
Sine comes from sinew- bowstring and is the measurement up a bow from a bowstring laid on a surface, to where an arrow (nocked at center) touches the bow
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