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

Problem

tan(√(,3)/3)

Solution

1. Identify the expression as the tangent of a constant value.

2. Rationalize the denominator of the argument to see if it matches a known trigonometric value, though √(,3)/3 is already the rationalized form of 1/√(,3)

3. Evaluate the numerical value of the argument. Since √(,3)≈1.732 the argument is approximately 1.732/3≈0.577 radians.

4. Determine if the expression can be simplified further. Because √(,3)/3 is not a standard multiple of π the expression tan(√(,3)/3) cannot be simplified to a cleaner exact algebraic form or a rational number.

Final Answer

tan(√(,3)/3)=tan(√(,3)/3)

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