What is Inverse Sine Function?

The inverse sine function is like a math operation that does the opposite of the regular sine function. It’s part of a group of functions called inverse trigonometric functions. Another name for it is arcsine which is pronounced as “arc sin”. In mathematical terms, it can be written as “asin x”, “sin^-1x”, or “arcsine x”. When written as “sin-1x,” it means “sin inverse of x.”

In an equation like sin x = y, one can use the inverse sine function to find x. So, if sin x = y, then x = sin^-1(y). It’s like switching sin from one side of the equation to the other.

Inverse Sine Definition

The inverse sine function is a mathematical operation that, when applied to a certain value, gives another value such that if you take the sine of that result, you get back to the original value. It is like a mathematical operation that undoes the sine operation, allowing you to find the angle associated with a given sine value.

y = sin x

⇒ x = sin^-1y

Inverse Sine Formula

In a right-angled triangle, the sine of an angle (θ) is the ratio of the opposite side to the hypotenuse (sin θ = opposite side / hypotenuse). The inverse sine function, denoted as θ = sin⁻¹[(opposite side) / (hypotenuse)], helps find the angle when the opposite side and hypotenuse are known. This function is expressed as θ = arcsin[(opposite side) / (hypotenuse)]. It’s used not only in right-angled triangles but also in any triangle through the sine law. In a triangle ABC, where AB = c, BC = a, and CA = b, sin A = (a sin B) / b, and A = sin⁻¹[(a sin B) / b].

θ = sin^-1 (opposite side/hypotenuse)

This formula is used in the context of a right-angled triangle, where θ represents an angle, and the inverse sine function helps find the angle when the lengths of the opposite side and the hypotenuse are known. The result θ is the measure of the angle in degrees or radians, depending on the context.

Read more about Inverse Trigonometric Functions

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”.