Evaluate arcsin(0.1)

Problem

arcsin(0.1)

Solution

1. Identify the expression as the inverse sine of 0.1 which represents the angle θ such that sin(θ)=0.1 within the interval [−π/2,π/2]

2. Recognize that 0.1 is not a standard value from the unit circle (like 0.5 or √(,2)/2, so a numerical approximation is required.

3. Calculate the value using a calculator or Taylor series expansion for arcsin(x)≈x+(x3)/6+(3*x5)/40

4. Convert the result to the desired format, typically radians or degrees. In radians, 0.1+0.001/6≈0.100167

Final Answer

arcsin(0.1)≈0.100167

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