Solve for x x=arctan(( square root of 3)/3)

Problem

x=arctan(√(,3)/3)

Solution

1. Identify the value inside the inverse tangent function. We are looking for an angle x such that tan(x)=√(,3)/3 within the principal range of the arctangent function, which is (−π/2,π/2)

2. Rationalize or rewrite the expression to recognize it from the unit circle. Note that √(,3)/3 is equivalent to 1/√(,3)

3. Relate the tangent value to sine and cosine. Since tan(x)=sin(x)/cos(x) we look for an angle where the ratio of the y-coordinate to the x-coordinate on the unit circle is 1/√(,3)

4. Determine the angle. For the angle x=π/6 (or 30, we have sin(π/6)=1/2 and cos(π/6)=√(,3)/2

5. Verify the ratio:

1/2/√(,3)/2=1/√(,3)=√(,3)/3

Final Answer

x=arctan(√(,3)/3)=π/6

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