Find the Exact Value arctan(( square root of 3)/3)

Problem

arctan(√(,3)/3)

Solution

1. Identify the definition of the inverse tangent function, where y=arctan(x) means tan(y)=x for y in the interval (−π/2,π/2)

2. Rewrite the expression as an equation to find the angle y such that tan(y)=√(,3)/3

3. Rationalize or recognize the equivalent form of the value, noting that √(,3)/3=1/√(,3)

4. Recall the trigonometric values for standard angles, specifically that tan(π/6)=sin(π/6)/cos(π/6)=(1/2)/(√(,3)/2)=1/√(,3)

5. Verify that the angle π/6 falls within the restricted range (−π/2,π/2)

Final Answer

arctan(√(,3)/3)=π/6

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