How is sinθ defined in trigonometry?

In trigonometry, the sine of an angle, denoted as sinθ, is defined as the ratio of the length of the side opposite the angle (the opposite side) to the length of the hypotenuse of the right triangle. This relationship can be understood as follows: in a right triangle, the hypotenuse is always the longest side, and it is the side opposite the right angle. The sine function specifically measures how 'tall' the triangle is relative to this hypotenuse when considering an angle θ.

The ratio is expressed mathematically as:

sinθ = (length of the opposite side) / (length of the hypotenuse)

This definition is fundamental in trigonometry and is used in various applications, such as calculating lengths and angles in triangles, modeling periodic phenomena, and in physics. Understanding this key concept allows for the solving of many problems that involve right triangles and their properties.

The other options mistakenly attribute the definitions to different relationships between the triangle's sides.