Find the Exact Value cot(240 degrees )

Problem

cot(240)

Solution

1. Identify the reference angle by determining the quadrant of 240 Since 180<240<270 the angle is in the third quadrant.

2. Calculate the reference angle θ′ using the formula θ′=θ−180

θ′=240−180=60

3. Determine the sign of the cotangent function in the third quadrant. In the third quadrant, both sine and cosine are negative, so their ratio cot(θ)=cos(θ)/sin(θ) is positive.

4. Evaluate the cotangent of the reference angle using known trigonometric values.

cot(60)=1/√(,3)

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

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

Final Answer

cot(240)=√(,3)/3

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