Find the Exact Value arcsin(2/3)

Problem

arcsin(2/3)

Solution

1. Identify the nature of the expression. The function arcsin(x) (or sin(x)(−1) represents the angle θ in the interval [−π/2,π/2] such that sin(θ)=2/3

2. Check for standard values. The value 2/3 is not a coordinate from the standard unit circle (such as 0,±1/2,±√(,2)/2,±√(,3)/2,±1.

3. Determine if further simplification is possible. Since 2/3 is not a standard trigonometric ratio, the exact value cannot be expressed in terms of common multiples of π

4. Conclude that the expression is already in its simplest exact form.

Final Answer

arcsin(2/3)=arcsin(2/3)

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