The sine function, denoted as sin x, is equal to zero at specific points along the x-axis on the unit circle. To find out when sin x = 0, we need to understand the periodic nature of the sine function.
Sin x is equal to zero at integer multiples of π (pi). This means that:
- x = nπ, where n is any integer (…, -3, -2, -1, 0, 1, 2, 3,…).
To explain further, when you look at the unit circle, the sine of an angle corresponds to the y-coordinate of a point on the circle. The points where this y-coordinate is zero are located along the x-axis. Therefore, these points occur at angles of 0, π, 2π, -π, -2π, and so on. In terms of radians, this gives us the values of x at which sin x equals zero.
In summary, sin x = 0 at:
x = nπ, where n ∈ ℤ (any integer)