Simplify arctan( square root of 3)

Problem

arctan(√(,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. Set up the equation to find the angle y such that tan(y)=√(,3)

3. Recall the values of trigonometric functions for special angles in the first quadrant.

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

5. Verify that π/3 falls within the required range (−π/2,π/2)

Final Answer

arctan(√(,3))=π/3

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