Final answer:
The solutions of the equation tan x = 0 are x = 0, π, 2π, and so on.
Step-by-step explanation:
To find all solutions of the equation tan x = 0, we need to determine the values of x for which the tangent of x is equal to zero.
Since the tangent of an angle is equal to the sine of the angle divided by the cosine of the angle, we can rewrite the equation as sin x / cos x = 0.
For the tangent to be equal to zero, the sine of x must be zero.
The unit circle provides us with the angles where the sine is zero, which are x = 0, π, 2π, ... and so on.
These are the solutions to the equation.