Find all solutions of the equation in the interval 1 27 pi S

Find all solutions of the equation in the interval [1, 27 pi). Squareroot 3 sec theta + 2 = 0 Write your answer in radians in terms of pi. If there is more than one solution, separate them with commas.

Solution

(sqrt 3) sec theta + 2 = 0

subtracting 2 from both sides

sqrt 3 sec theta = -2

sec theta = -2 / sqrt 3

theta = 5pi/6 + 2pi*n , 7 pi/6 + 2pi*n

solutions are

theta = 7pi/6 , 5pi/6