2023年11月21日 · Arcsin function is the inverse function of the sine function. The inverse of sin gives the angle that has the given sine value. Therefore, in a triangle, the arcsin or sin^{-1} function takes ...

2018年12月4日 · $\arcsin$ is the better notation I feel, because many students think that they are equal $$\sin^{-1}(x) \neq \frac{1}{\sin(x)}$$ when in fact $\arcsin(x)$ (or $\sin^{-1}(x)$) is the unique function so that: $$\arcsin(\sin(x)) = \sin(\arcsin(x)) = x $$ Now to address your other question. $\arcsin(x)$ IS a function.

2017年4月29日 · 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 &\\text{or ...

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!

2018年9月15日 · These functions are the inverse of their respective trigonometric functions. As such they are multiple valued

2017年11月27日 · 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 ...

2015年9月24日 · Starting from the well-known power series of $\arcsin$, \begin{equation} \newcommand{\where}[1]{\qquad(#1)} \newcommand{\abs}[1]{\lvert#1\rvert} \newcommand ...

This may be clearer if we plot out arcsin x, or, as we learned above, sin y = x. Keep in mind y is the angle in radians. For y = 0, sin y = sin 0 = 0 so x = 0 for y = 0

Since $\sin(x)$ is always in the interval $[-1,1]$ where $\arcsin$ is defined, $\arcsin(\sin(x))$ is ...

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.