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The arcsine reverses the input and output of the sine function, so that the arcsine has domain \(D=[-1,1]\) and range \(R=\left[\dfrac{-\pi}{2},\dfrac{\pi}{2}\right]\). The graph of the arcsine is drawn below.
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Graph the function with the calculator. ... 19.1: The...
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Solution steps. Vertical asymptotes of arcsin(x): None. Horizontal Asymptotes of arcsin(x): None. Slant Asymptotes of arcsin(x): None. None. Enter your problem. Popular Examples.
The inverse sine function is sometimes called the arcsine function, and notated \(\arcsin\space x\). \(y={\sin}^{−1}x\) has domain \([−1,1]\) and range \(\left[−\frac{\pi}{2},\frac{\pi}{2}\right]\)
The Inverse Sine Function (arcsin) We define the inverse sine function as `y=arcsin\ x` for `-pi/2<=y<=pi/2` where y is the angle whose sine is x. This means that `x = sin y` The graph of y = arcsin x. Let's see the graph of y = sin x first and then derive the curve of y = arcsin x.
15 cze 2021 · To find \(\arcsin\left(-\frac{1}{2}\right)\), we seek the number \(t\) in the interval \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) with \(\sin(t) = -\frac{1}{2}\). The answer is \(t = -\frac{\pi}{6}\) so that \(\arcsin\left(-\frac{1}{2}\right) = -\frac{\pi}{6}\).
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As we see the magnitude of $\tan(x)$ growing without bound (either in a positive or negative way) as $x$ approaches each odd multiple of $\frac{\pi}{2}$, we can expect to see some vertical asymptotes in its graph.
