What values satisfy the equation tan x = 0?

To determine the values that satisfy the equation tan x = 0, it’s essential to understand the properties of the tangent function. The tangent function, which is the ratio of the sine and cosine functions (tan x = sin x / cos x), equals zero whenever the sine function equals zero, since any number divided by zero is undefined.

The sine function equals zero at integer multiples of π (or 180 degrees). Specifically, sine is zero at angles 0°, ±180°, ±360°, and so on. Therefore, the angles that satisfy tan x = 0 correspond to these angles.

Since the correct answer identifies the values 0, ±180°, and ±360°, it encompasses all the angles where the sine function is zero, reinforcing that these angles will result in the tangent function being zero as well. The inclusion of both positive and negative angles recognizes the periodic nature of the tangent function, which is periodic with a period of 180 degrees or π radians.

In contrast, other choices provide values that do not satisfy tan x = 0 based on the sine function’s properties. For instance, angles like ±90° and ±270° correspond to the points where the cosine function is zero, leading to the tangent function being undefined rather