In trigonometry, what does 'sin' stand for?

The term 'sin' in trigonometry stands for the sine function, which is defined as the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. This fundamental relationship is crucial in the study of trigonometry as it helps describe the nature of angles and side lengths in right triangles.

In a right-angled triangle, if you have an angle, the side opposite that angle is referred to as the opposite side, while the longest side of the triangle, which is opposite the right angle, is called the hypotenuse. Thus, the correct formulation of the sine function is the ratio of the length of the opposite side to the hypotenuse. Understanding this allows students to apply sine in various mathematical contexts, including solving problems related to angles and lengths in triangles.

This foundational principle is key to advancing in trigonometry and serves as the cornerstone for further concepts, such as the unit circle, wave functions, and many applications in physics and engineering.