Domain and Range of Inverse Sine
The domain is the input value for which inverse sine function is defined and range is the corresponding value for that domain. The domain and range of Inverse sine function is discussed below:
Domain of Inverse Sine
The domain of the inverse sine function, often denoted as sin-1x, is the set of real numbers from -1 to 1, inclusive. In mathematical terms, it is represented as [-1, 1]. This means that you can input any value within this range into the inverse sine function.
Range of Inverse Sine
The range of the inverse sine function, denoted as sin{-1}x or arcsin x, is the set of real numbers from -π/2 to π/2, inclusive. In mathematical terms, it is represented as -π/2, π/2. This signifies the possible output values or angles that the inverse sine function can yield when given inputs from the domain [-1, 1].
How to Find Sin Inverse x
To find the sin inverse of x:
- Recognize that the possible answers lie in the range of [-π/2, π/2].
- Let’s assume y is the sin inverse of x, denoted as y = sin⁻¹x. According to the definition of inverse sine, this means sin y = x.
- Consider values of y within the interval [-π/2, π/2] that satisfy the equation sin y = x. The solution lies in this range.
Inverse Sine
Inverse Sine function is one of the important inverse trigonometric functions. The inverse of trigonometric functions gives the angle with the help of the sides of the triangles. In this article, we will explore the inverse sine function, its definition, formula, and properties. We will also discuss the domain and range of the inverse sine function, the graph of the inverse sine function, the derivative of inverse sine, and the integral of inverse sine along with the solved examples. Let’s start our learning on the topic of “Inverse Sine”.
Table of Content
- What is Sine Function?
- What is Inverse Sine Function?
- Properties of Inverse Sine Function
- Domain and Range of Inverse Sine
- Graph of Inverse Sine Function
- Derivative and Integral of Inverse Sine
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