Find the Exact Value arcsin(0.5)

Problem

arcsin(0.5)

Solution

1. Identify the meaning of the inverse sine function, which asks for an angle θ in the interval [−π/2,π/2] such that sin(θ)=0.5

2. Convert the decimal value to a fraction to make it easier to recognize standard trigonometric values.

arcsin(0.5)=arcsin(1/2)

3. Recall the unit circle or special right triangles where the sine of an angle is 1/2

sin(30)=1/2

sin(π/6)=1/2

4. Verify that the angle π/6 falls within the restricted range of the arcsine function, which is [−π/2,π/2]

−π/2≤π/6≤π/2

Final Answer

arcsin(0.5)=π/6

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