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Arcsin x gives the measure of the angle corresponding to the ratio of the perpendicular and hypotenuse of a right-angled triangle. In this article, we will explore the concept of arcsin and derive its formula. We will also discuss the domain and range of arcsin x and hence, plot its graph.
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Arcsin graph. The graph of y = arcsin (x) is shown below: The domain of y = arcsin (x) is and its range is . One of the properties of inverse functions is that if a point (a, b) is on the graph of f, the point (b, a) is on the graph of its inverse.
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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 \(\left[−\frac{\pi}{2},\frac{\pi}{2}\right]\)
What is Inverse Sine? The inverse sine function is the inverse of the sine function and thus it is one of the inverse trigonometric functions. It is also known as arcsin function which is pronounced as "arc sin". It is mathematically written as "asin x" (or) "sin -1 x" or "arcsin x". We read "sin -1 x" as "sin inverse of x".
