Use the reference angle to find the exact value of the follo

Use the reference angle to find the exact value of the following expression. Do not use a calculator.
cot (-5pi^6)=?
Simplify your answer. Type an exact answer, jsing radicals as needed. Use integers or fractions for any numbers in the expression.

Solution

cot ( -5pi / 6 )

5pi/6 has reference angle of pi/6

cot ( -5pi/6) = cos ( -5pi/6) / sin ( -5pi/6 )

cos ( pi/6 ) = sqrt 3/2

cos ( -5pi/6 ) = sqrt 3 / 2

sin (pi/6) = 1/2

sin ( -5pi/6) = 1/2

plugging the values in the formula

cot (-5pi/6) = sqrt 3 / 2 / 1/2 = sqrt 3

cot ( -5pi/6) = sqrt 3