Find the Exact Value cot(-300 degrees )

Problem

cot(−300)

Solution

1. Find the coterminal angle by adding 360 to the negative angle to find an equivalent angle within the standard 0 to 360 range.

θ=−300+360=60

2. Identify the reference angle and the quadrant. Since 60 is in the first quadrant, the reference angle is 60 and all trigonometric functions are positive.

cot(−300)=cot(60)

3. Apply the definition of the cotangent function in terms of sine and cosine.

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

4. Substitute the known values for the sine and cosine of 60

cos(60)=1/2

sin(60)=√(,3)/2

5. Simplify the fraction by dividing the two values.

cot(60)=(1/2)/(√(,3)/2)=1/√(,3)

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

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

Final Answer

cot(−300)=√(,3)/3

Want more problems? Check here!