Find the Exact Value arccot( square root of 3)

Problem

arccot(√(,3))

Solution

1. Identify the definition of the inverse cotangent function, where y=arccot(x) means cot(y)=x for y in the interval (0,π)

2. Set up the equation based on the given value:

cot(y)=√(,3)

3. Rewrite the cotangent function in terms of sine and cosine to relate it to known values on the unit circle:

cos(y)/sin(y)=√(,3)

4. Determine the angle y in the first quadrant that satisfies this ratio. Since cos(π/6)=√(,3)/2 and sin(π/6)=1/2 we have:

√(,3)/2/1/2=√(,3)

5. Conclude that the angle y is π/6

Final Answer

arccot(√(,3))=π/6

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