Simplify 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. Evaluate the exact values of the cosine and sine of 60^∘ using the unit circle or a special right triangle.

cos(60^∘)=1/2

sin(60^∘)=√(,3)/2

4. Simplify the resulting fraction by dividing the two values.

cot(60^∘)=1/2/√(,3)/2

cot(60^∘)=1/√(,3)

5. 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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