Find the Exact Value arcsin(1/5)

Problem

arcsin(1/5)

Solution

1. Identify the expression as an inverse trigonometric function, which represents the angle θ such that sin(θ)=1/5 within the restricted range [−π/2,π/2]

2. Determine if the value 1/5 corresponds to a standard angle on the unit circle (such as 0,1/2,√(,2)/2,√(,3)/2,1.

3. Conclude that since 1/5 is not a standard value, the exact value cannot be simplified into a rational multiple of π or a simpler radical form.

4. State the result in its simplest exact form using the inverse sine notation.

Final Answer

arcsin(1/5)=arcsin(1/5)

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