What is the sine value of 30°?

The sine value of 30° is 0.5, which can be understood through the properties of a right triangle or the unit circle.

In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. For a 30° angle in a special 30°-60°-90° triangle, the opposite side is half the length of the hypotenuse. Specifically, if the hypotenuse is 1 unit, the side opposite to the 30° angle would be 0.5 units, leading to the sine of 30° being calculated as:

[

\sin(30°) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{0.5}{1} = 0.5

]

In the context of the unit circle, the sine of an angle also represents the y-coordinate of the point on the circle corresponding to that angle. For 30°, the coordinates of the point on the unit circle are ((\frac{\sqrt{3}}{2}, \frac{1}{2})), confirming that the sine value (the y-coordinate