Find the Exact Value cot((-pi)/3)

Problem

cot(−π/3)

Solution

1. Identify the periodicity and parity of the cotangent function. Since cotangent is an odd function, cot(−x)=−cot(x)

cot(−π/3)=−cot(π/3)

2. Express the cotangent function in terms of sine and cosine.

cot(π/3)=cos(π/3)/sin(π/3)

3. Substitute the known values for the trigonometric functions at π/3

cos(π/3)=1/2

sin(π/3)=√(,3)/2

4. Calculate the value of the cotangent by dividing the fractions.

cot(π/3)=(1/2)/(√(,3)/2)

cot(π/3)=1/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

cot(π/3)=√(,3)/3

6. Apply the negative sign from the first step to find the final value.

cot(−π/3)=−√(,3)/3

Final Answer

cot(−π/3)=−√(,3)/3

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