Math Problem Statement

-y = sin^(-1)(x)

Solution

The equation in the image is:

y=sin1(x)-y = \sin^{-1}(x)

This is the inverse sine function, also known as the arcsine function. The equation can be rewritten as:

y=sin1(x)y = -\sin^{-1}(x)

This means that yy is equal to the negative of the arcsine of xx.

Would you like more details on how to solve for yy, or on the properties and graph of this function? Let me know if you have any questions.

Here are some related questions:

  1. What is the domain and range of the function y=sin1(x)y = -\sin^{-1}(x)?
  2. How does the graph of y=sin1(x)y = -\sin^{-1}(x) compare to the graph of y=sin1(x)y = \sin^{-1}(x)?
  3. Can you express y=sin1(x)y = -\sin^{-1}(x) in terms of a trigonometric function of an angle?
  4. What is the derivative of y=sin1(x)y = -\sin^{-1}(x) with respect to xx?
  5. What is the integral of y=sin1(x)y = -\sin^{-1}(x) with respect to xx?

Tip: The arcsine function sin1(x)\sin^{-1}(x) returns the angle whose sine is xx, with the angle measured in radians.

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Math Problem Analysis

Mathematical Concepts

Inverse Trigonometric Functions
Arcsine Function
Equation Manipulation

Formulas

y = -sin^(-1)(x)

Theorems

-

Suitable Grade Level

Grades 10-12