Solve the following equation in the interval [0, 2 \\pi]. Note: Give the answer
ID: 3399862 • Letter: S
Question
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. | an(t)|= rac{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.
Explanation / Answer
| 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