Simplify arctan(1/( square root of 3))

Problem

arctan(1/√(,3))

Solution

1. Identify the goal as finding the angle θ such that tan(θ)=1/√(,3) within the restricted range of the arctangent function, which is (−π/2,π/2)

2. Rationalize the expression if necessary to recognize standard values, though 1/√(,3) is already a common ratio for trigonometric functions.

3. Recall the values of the tangent function for standard angles in the first quadrant.

4. Determine that tan(π/6)=sin(π/6)/cos(π/6)=(1/2)/(√(,3)/2)=1/√(,3)

5. Conclude that since π/6 falls within the interval (−π/2,π/2) it is the principal value.

Final Answer

arctan(1/√(,3))=π/6

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