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

Problem

arctan(√(,3)/3)

Solution

1. Identify the value inside the inverse tangent function and recognize it as a standard trigonometric ratio.

2. Rationalize or rewrite the expression to see its more common form by noting that √(,3)/3 is equivalent to 1/√(,3)

3. Recall the unit circle values for the tangent function, where tan(θ)=sin(θ)/cos(θ)

4. Determine the angle θ in the restricted range of the arctangent function, (−π/2,π/2) such that tan(θ)=1/√(,3)

5. Evaluate the angle, noting that sin(π/6)=1/2 and cos(π/6)=√(,3)/2

6. Calculate the ratio:

1/2/√(,3)/2=1/√(,3)=√(,3)/3

7. Conclude that the angle is π/6

Final Answer

arctan(√(,3)/3)=π/6

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