Find the Exact Value cot(-60 degrees )

Problem

cot(−60)

Solution

1. Apply the odd-even property of the cotangent function, which states that cot(−θ)=−cot(θ)

cot(−60)=−cot(60)

2. Use the definition of cotangent in terms of sine and cosine.

cot(60)=cos(60)/sin(60)

3. Substitute the known values for the sine and cosine of 60 from the unit circle, where cos(60)=1/2 and sin(60)=√(,3)/2

cot(60)=1/2/√(,3)/2

4. Simplify the fraction by canceling the denominators.

cot(60)=1/√(,3)

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

cot(60)=√(,3)/3

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

−cot(60)=−√(,3)/3

Final Answer

cot(−60)=−√(,3)/3

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