Find the Inverse y=sin(x)

Problem

y=sin(x)

Solution

1. Swap the variables x and y to begin finding the inverse relationship.

x=sin(y)

2. Apply the inverse sine function, also known as arcsine, to both sides of the equation to isolate y

arcsin(x)=arcsin(sin(y))

3. Simplify the right side using the property that arcsin(sin(y))=y within the restricted domain [−π/2,π/2]

arcsin(x)=y

4. Rewrite the equation in standard function notation for an inverse.

y=arcsin(x)

Final Answer

y=arcsin(x)

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