Evaluate cot(420 degrees )

Problem

cot(420)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to find an equivalent angle within the first rotation.

θ=420−360=60

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

cot(θ)=cos(θ)/sin(θ)

3. Substitute the reference values for 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 multiplying by the reciprocal of the denominator.

cot(60)=1/√(,3)

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

cot(60)=√(,3)/3

Final Answer

cot(420)=√(,3)/3

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