Solve for x y=sin(x)

Problem

y=sin(x)

Solution

1. Identify the goal, which is to isolate the variable x in the equation y=sin(x)

2. Apply the inverse function by taking the arcsine (inverse sine) of both sides of the equation.

3. Simplify the right side using the property that arcsin(sin(x))=x within the restricted domain of the inverse function.

4. State the general solution by accounting for the periodicity of the sine function, where n is any integer.

Final Answer

x=(−1)n*arcsin(y)+n*π

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