Solve the following equation in the interval [0, 2 pi].

Question

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)| = 1/sqrt(3)

Answer 1

The equation |tan(t)| = 1/sqrt(3) can be rewritten as tan(t) = 1/sqrt(3) or tan(t) = -1/sqrt(3).

First, let's solve the equation tan(t) = 1/sqrt(3):
t = pi/6 + k*pi, where k is an integer.

Next, let's solve the equation tan(t) = -1/sqrt(3):
t = 5*pi/6 + k*pi, where k is an integer.

Therefore, the solutions in the interval [0, 2 pi] are:
t = pi/6, 5*pi/6, 7*pi/6, 11*pi/6.