Find the Exact Value cot(600)

Problem

cot(600^∘)

Solution

1. Find the coterminal angle by subtracting multiples of 360^∘ until the angle is between 0^∘ and 360^∘

600^∘−360^∘=240^∘

2. Identify the quadrant for 240^∘ Since 180^∘<240^∘<270^∘ the angle lies in Quadrant III.

3. Determine the reference angle for an angle in Quadrant III using the formula (θ_ref)=θ−180^∘

240^∘−180^∘=60^∘

4. Determine the sign of the cotangent function in Quadrant III. Cotangent is positive in Quadrant III.

cot(600^∘)=cot(60^∘)

5. Evaluate the exact value using the definition cot(θ)=cos(θ)/sin(θ) or the known value for 60^∘

cot(60^∘)=1/√(,3)

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

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

Final Answer

cot(600^∘)=√(,3)/3

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