Find the Exact Value arctan(1/2)

Problem

arctan(1/2)

Solution

1. Identify the expression as the inverse tangent function, which represents the angle θ such that tan(θ)=1/2 within the interval (−π/2,π/2)

2. Check for standard unit circle values. The value 1/2 is not a standard ratio for tangent (such as 0 √(,3)/3 1 or √(,3).

3. Determine if a simpler form exists. Since 1/2 is not a standard trigonometric ratio, the exact value cannot be expressed in terms of simple fractions of π

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

Final Answer

arctan(1/2)=arctan(1/2)

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