Find the Exact Value cot(-(7pi)/12)

Problem

cot(−(7*π)/12)

Solution

1. Use the odd-even property of the cotangent function, which states cot(−θ)=−cot(θ)

cot(−(7*π)/12)=−cot((7*π)/12)

2. Rewrite the angle as a sum of two special angles from the unit circle.

(7*π)/12=(3*π)/12+(4*π)/12=π/4+π/3

3. Apply the cotangent sum formula, cot(A+B)=(cot(A)*cot(B)−1)/(cot(B)+cot(A))

−cot(π/4+π/3)=−(cot(π/4)*cot(π/3)−1)/(cot(π/3)+cot(π/4))

4. Substitute the known values cot(π/4)=1 and cot(π/3)=√(,3)/3

−(1⋅√(,3)/3−1)/(√(,3)/3+1)

5. Simplify the fraction by multiplying the numerator and denominator by 3

−(√(,3)−3)/(√(,3)+3)

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

−((√(,3)−3)2)/((√(,3)+3)*(√(,3)−3))

7. Expand and simplify the expression.

−(3−6√(,3)+9)/(3−9)

−(12−6√(,3))/(−6)

2−√(,3)

Final Answer

cot(−(7*π)/12)=2−√(,3)

Want more problems? Check here!