Solve the following equation in the interval 0 2 pi Note Giv

Solve the following equation in the interval [0, 2 \\pi]. Note: Give the answer as a multiple of \\pi. Do not use decimal numbers. The answer should be a fraction or an integer. Note that \\pi is already included in the answer so you just have to enter the appropriate multiple. E.g. if the answer is \\pi/2 you should enter 1/2. If there is more than one answer enter them separated by commas. |\\tan(t)|=\\frac{1}{\\sqrt(3)} t = 1/6,7/6,5/6 \\pi i have 3 of them but cant figure out the 4th solution to this question.

Solution

| tant | = 1/sqrt3

+ve tant = 1/sqrt3

t = tan^-1(1/sqrt3) = pi/6 ,pi+pi/6 = pi/6 , 7pi/6

-ve tant = -1/sqrt3

t = tan^-1(-1/sqrt3)

= pi- pi/6 , 2pi-pi/6 ( tant is -ve in IInd and IVrth quadrant)

= 5pi/6 , 11pi/6

Solution : pi/6 , 7pi/6 , 5pi/6 , 11pi/6