sin180

sin180 refers to the sine of an angle measuring 180 degrees. In trigonometry, the sine function is a ratio of the length of the side opposite an angle to the length of the hypotenuse in a right-angled triangle. However, when considering angles beyond 90 degrees, we often use the unit circle to define trigonometric functions. The unit circle is a circle with a radius of 1 centered at the origin of a Cartesian coordinate system. For any angle theta measured counterclockwise from the positive x-axis, the sine of theta is the y-coordinate of the point where the terminal side of the angle intersects the unit circle.

At 180 degrees, the terminal side of the angle lies along the negative x-axis. The point where this ray intersects the unit circle is at coordinates (-1, 0). Therefore, the y-coordinate of this point is 0. Consequently, sin180 is equal to 0. This value is consistent across various mathematical contexts and is a fundamental result in trigonometry. It is often used in calculations involving trigonometric identities and in the analysis of periodic functions. The sine function has a period of 360 degrees (or 2π radians), meaning its values repeat every full circle.