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

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