Find the Exact Value cot(300 degrees )

Problem

cot(300)

Solution

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

360−300=60

2. Determine the quadrant in which 300 lies. Since 270<300<360 the angle is 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. Apply the definition of cotangent as the ratio of cosine to sine for the reference angle.

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

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

cot(60)=(1/2)/(√(,3)/2)

6. Simplify the fraction.

cot(60)=1/√(,3)

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

cot(60)=√(,3)/3

8. Combine the value with the negative sign determined in step 3.

cot(300)=−√(,3)/3

Final Answer

cot(300)=−√(,3)/3

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