Evaluate cot(120 degrees )

Problem

cot(120)

Solution

1. Identify the reference angle by finding the difference between 120 and the nearest x-axis value (180.

180−120=60

2. Determine the quadrant of the angle 120 which lies in Quadrant II.

3. Determine the sign of the cotangent function in Quadrant II, where cotangent is negative.

cot(120)=−cot(60)

4. Recall the trigonometric identity for cotangent in terms of sine and cosine.

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 to find the value of the reference angle.

cot(60)=1/√(,3)

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

cot(60)=√(,3)/3

8. Apply the negative sign determined in step 3.

cot(120)=−√(,3)/3

Final Answer

cot(120)=−√(,3)/3

Want more problems? Check here!