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For what values of θ is the tangent 0?

For what values of θ is the tangent undefined?
please please explain

tanx = 0 for x = 0 + nπ

tanx is undefined for x = π/2 + nπ

Did you know?

Did you know that the tangent function, denoted as tan(θ), can have special values for certain angles? When we say that the tangent is 0 for a particular angle, we refer to the fact that tan(θ) = 0. This occurs when the angle θ is a multiple of 180 degrees, or π radians. On these angles, the tangent line of the unit circle intersects the x-axis, resulting in a value of zero. On the other hand, did you know that the tangent function is undefined for some angles? This happens when the tangent line becomes vertical, leading to a situation where the ratio of the y-coordinate to the x-coordinate is indeterminate. These angles occur when the angle θ is a multiple of 90 degrees, or π/2 radians. At these angles, the tangent function is not defined, hence its value is undefined. Understanding when the tangent is zero or undefined can be particularly useful in various applications of trigonometry, such as solving equations, analyzing graphs, or studying the behavior of functions.