Simplify arccot(1/( square root of 3))

Problem

arccot(1/√(,3))

Solution

1. Identify the definition of the inverse cotangent function. The expression y=arccot(x) is equivalent to cot(y)=x where y is an angle typically in the interval (0,π)

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

cot(y)=1/√(,3)

3. Relate the cotangent function to the sine and cosine functions.

cos(y)/sin(y)=1/√(,3)

4. Recall the values of trigonometric functions for standard angles. For the angle y=π/3 (or 60:

cos(π/3)=1/2

sin(π/3)=√(,3)/2

5. Verify the ratio for the cotangent of π/3

cot(π/3)=(1/2)/(√(,3)/2)

cot(π/3)=1/√(,3)

6. Conclude that the angle y is π/3

Final Answer

arccot(1/√(,3))=π/3

Want more problems? Check here!