Find the Exact Value cot(60)

Problem

cot(60)

Solution

1. Identify the trigonometric identity for the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

2. Substitute the specific angle of 60 into the identity.

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

3. Recall the exact values for the sine and cosine of 60 from the unit circle or a special right triangle.

cos(60)=1/2

sin(60)=√(,3)/2

4. Substitute these values into the fraction.

cot(60)=1/2/√(,3)/2

5. Simplify the complex fraction by multiplying by the reciprocal of the denominator.

cot(60)=1/2⋅2/√(,3)

cot(60)=1/√(,3)

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

cot(60)=(1⋅√(,3))/(√(,3)⋅√(,3))

cot(60)=√(,3)/3

Final Answer

cot(60)=√(,3)/3

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