If y = sin^(-1)(x), then x = sin(y) implies:

₹0.0

Question: If y = sin^(-1)(x), then x = sin(y) implies:

Options:

Correct Answer: y = x

Solution:

By definition, if y = sin^(-1)(x), then x = sin(y).

If y = sin^(-1)(x), then x = sin(y) implies:

If y = sin^(-1)(x), then x = sin(y) implies:

Step 1: Understand that sin^(-1)(x) means the inverse sine function, which gives you an angle y such that sin(y) = x.
Step 2: If we say y = sin^(-1)(x), it means we have found an angle y for which the sine of that angle equals x.
Step 3: The equation x = sin(y) is simply stating that if you take the sine of the angle y, you will get back x.
Step 4: Therefore, by the definition of the inverse sine function, if y = sin^(-1)(x), then it is true that x = sin(y).

Inverse Trigonometric Functions – Understanding the relationship between a function and its inverse, specifically how the sine function and its inverse (arcsine) relate to each other.
Function Definition – Recognizing that the definition of the arcsine function directly leads to the equality x = sin(y) when y is defined as sin^(-1)(x).