The sine function, denoted as sin(x), equals zero at specific intervals on the unit circle. Understanding when this occurs is essential, especially in trigonometry and calculus.
In mathematical terms, sin(x) = 0 at the following points:
x = n imes \\pifor any integern.
This means that sine is zero at:
0, \\pi, 2\\pi, -\\pi, -2\\pi, \\frac{3\\pi}{2}, ...
Graphically, you can visualize this: every whole multiple of \\pi represents a point on the unit circle where the y-coordinate (which corresponds to the sine value) is zero. So, whether you are looking at 0 radians, or moving in increments of \\pi (which is about 3.14), the sine function will cross the x-axis at these values.
This property of the sine function is crucial for solving equations involving sine, especially when you’re asked to determine the angles where sine equals zero in any given interval.
In summary, sine of x equals zero whenever x is a multiple of \\pi.