Find the Exact Value cot(300)

Problem

cot(300)

Solution

1. Identify the reference angle by finding the difference between 300 and the nearest x-axis angle, which is 360

360−300=60

2. Determine the quadrant of the angle. Since 300 is between 270 and 360 it lies in Quadrant IV.

3. Determine the sign of the cotangent function in Quadrant IV. In this quadrant, cosine is positive and sine is negative, so cotangent is negative.

cot(300)=−cot(60)

4. Evaluate the cotangent of the reference angle using the definition cot(θ)=cos(θ)/sin(θ)

cot(60)=cos(60)/sin(60)

5. Substitute the known values cos(60)=1/2 and sin(60)=√(,3)/2

cot(60)=(1/2)/(√(,3)/2)

6. Simplify the fraction and rationalize the denominator.

cot(60)=1/√(,3)

cot(60)=√(,3)/3

7. Apply the negative sign determined in step 3.

cot(300)=−√(,3)/3

Final Answer

cot(300)=−√(,3)/3

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