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Here, we will study in detail about the inverse sine function (sin inverse) along with its graph, domain, range, and properties. Also, we will learn the formulas, derivatives, and integral of sin inverse x along with a few solved examples for a better understanding of the concept.
25 Μαρ 2021 · Find the exact value of expressions involving the inverse sine, cosine, and tangent functions. Use a calculator to evaluate inverse trigonometric functions. Find exact values of composite functions with inverse trigonometric functions.
Considering the domain and range of the inverse functions, following formulas are important to be noted: sin (sin-1x) = x, if -1 ≤ x ≤ 1 and sin-1 (sin y) = y if -π/2 ≤ y ≤ π/2. cos (cos -1x) = x, if -1 ≤ x ≤ 1 and cos -1(cos y) = y if 0 ≤ y ≤ π. tan (tan -1x) = x, if -∞ < x < ∞ and cos -1(cos y) = y if -π/2 ≤ y ≤ π/2.
9 Ιαν 2023 · A step-by-step guide to graphing the inverse of the sine function. The inverse sine function (also called arcsine) is the inverse of the sine function. It is mathematically written as \(asin x\) (or) \(sin^{-1}x\) or \(arcsin x\). We read \(sin^{-1}x\) as “\(sin\) inverse of \(x\)”. \(arcsin\:x=\:sin^{-1}x\:=\:inverse\:of\:sin\:x\)
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.
12 Αυγ 2024 · The graph of the inverse sine function, \(y=\sin ^{-1} \left(x\right)\), is shown below. Its domain is the same as the range of the sine function, namely \(-1 \leq x \leq 1\), and its range is our restricted domain for the sine, \(-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}\).
Consider the graphs of \(\sin^{-1} x\) and \(\tan^{-1} x\). Do these graphs satisfy any properties of symmetry? Are these functions either even, odd, or neither?
