Find the Exact Value arctan(3/2)

Problem

arctan(3/2)

Solution

1. Identify the expression as the inverse tangent of a positive ratio. The value arctan(3/2) represents the angle θ in the interval (−π/2,π/2) such that tan(θ)=3/2

2. Evaluate the ratio against known values of the tangent function for special angles (such as 0,π/6,π/4,π/3,π/2. Since 3/2=1.5 does not correspond to the tangent of a standard special angle (like 1 √(,3) or √(,3)/3, the value cannot be simplified into a simpler multiple of π

3. Conclude that the exact value is most accurately represented by the expression itself, as any decimal approximation would not be "exact."

Final Answer

arctan(3/2)=arctan(3/2)

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