Properties of Inverse Trigonometric Functions Video Lecture | Mathematics (Maths) Class 12 - JEE

Ans. The properties of inverse trigonometric functions are as follows: - The domain of inverse trigonometric functions is the range of the corresponding trigonometric functions. - The range of inverse trigonometric functions is the domain of the corresponding trigonometric functions. - Inverse trigonometric functions have restricted ranges to ensure one-to-one correspondence with their trigonometric counterparts. - The principal value of an inverse trigonometric function lies within a specific range, usually between -π/2 and π/2 for arcsin(x) and -π/2 and π/2 for arccos(x) and arctan(x). - Inverse trigonometric functions can be used to solve trigonometric equations and find the angles that satisfy certain trigonometric ratios.

Ans. Inverse trigonometric functions are closely related to trigonometric functions as they provide a way to find the angle (or angles) that satisfy a given trigonometric ratio. While trigonometric functions take an angle as input and provide the corresponding ratio as output, inverse trigonometric functions take a ratio as input and give the corresponding angle (or angles) as output. They essentially "undo" the effect of trigonometric functions, allowing us to find the angle(s) associated with a given ratio.

Ans. The restricted range of inverse trigonometric functions is significant because it ensures a one-to-one correspondence between the trigonometric functions and their inverses. By restricting the range, we avoid ambiguity and ensure that each value of the trigonometric function corresponds to a unique value of the inverse trigonometric function. This allows us to define inverse trigonometric functions as well-defined functions rather than relations.

Ans. Inverse trigonometric functions can be used to solve trigonometric equations by applying them to both sides of the equation. By doing so, we can isolate the angle and find its value. For example, if we have the equation sin(x) = 1/2, we can apply the arcsin function to both sides to obtain x = arcsin(1/2). This allows us to find the angle (or angles) that satisfy the equation.

Ans. Yes, inverse trigonometric functions can be used to find the angles of a triangle. By knowing the lengths of the sides of a triangle, we can use inverse trigonometric functions to find the angles. For example, if we have the lengths of two sides of a right triangle, we can use the arctan function to find the measure of the angle opposite the given sides. Similarly, the arcsin and arccos functions can be used to find angles in non-right triangles by knowing the lengths of the sides or the ratios of the sides.