Find the Exact Value sin(arcsin(1/4))

Problem

sin(arcsin(1/4))

Solution

1. Identify the composition of functions. The expression is of the form sin(arcsin(x)) where x=1/4

2. Apply the property of inverse trigonometric functions. For any value x in the domain of the inverse sine function, which is [−1,1] the identity sin(arcsin(x))=x holds true.

3. Verify the domain. Since 1/4 is between −1 and 1 the identity applies directly.

4. Evaluate the expression by substituting the value of x

Final Answer

sin(arcsin(1/4))=1/4

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