Find the Exact Value sin(arcsin(1/2))

Problem

sin(arcsin(1/2))

Solution

1. Identify the property of inverse trigonometric functions, which states that sin(arcsin(x))=x for all x in the domain of the inverse sine function.

2. Check if the input value x=1/2 falls within the domain of arcsin(x) which is the interval [−1,1]

3. Observe that since −1≤1/2≤1 the identity applies directly.

4. Evaluate the expression by simplifying the composition of the function and its inverse.

Final Answer

sin(arcsin(1/2))=1/2

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