Find the Exact Value cot(60 degrees )

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 angle 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.

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 canceling the common denominator of 2

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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