Which of the following values satisfies the equation sin x = 0?

To determine which values satisfy the equation sin x = 0, it's essential to understand the behavior of the sine function on the unit circle. The sine of an angle in a circle is defined as the y-coordinate of the point on the circumference corresponding to that angle measured from the positive x-axis.

The sine function equals zero at specific angles where the point lies on the x-axis, which occurs at integer multiples of 180 degrees. This means that at angles such as 0 degrees, 180 degrees, and 360 degrees, the sine value will indeed be zero.

When considering the periodicity of the sine function, we find that it will also equal zero at angles like -180 degrees and -360 degrees due to its symmetry. Therefore, the correct set of values that result in sin x = 0 includes ±180 degrees and ±360 degrees.

The other choices, such as 0 and 90, or 90 and 270, do not meet the criterion since they do not fulfill the condition of sine being zero. 0 degrees results in sin 0 = 0, but 90 degrees yields sin 90 = 1. Similarly, 90 and 270 do not work because although sin 270 = -