sin120

sin120 refers to the sine of the angle 120 degrees, which is a common value in trigonometry. The angle 120° lies in the second quadrant of the unit circle where sine values are positive. Using the identity sin(180° – θ) = sin θ, sin120° equals sin60°. The exact value of sin60° is √3⁄2, so sin120° also equals √3⁄2, approximately 0.8660254038.

In radian measure, 120° corresponds to 2π⁄3 radians, so sin(2π⁄3) has the same value of √3⁄2. This value appears frequently in problems involving equilateral triangles, 30‑60‑90 right triangles, and in the resolution of vectors into components. The sine function’s periodicity of 360° (or 2π radians) means that sin(120° + 360° k) = √3⁄2 for any integer k.

The graph of sin θ rises from zero at 0°, reaches a maximum of 1 at 90°, then decreases to √3⁄2 at 120°, returning to zero at 180°. Thus at the 120° mark the sine curve is symmetric with respect to the x‑axis at 90°, indicating that angles π⁄3 and 2π⁄3 share the same sine value.

Applications of sin120 include computing the height of a component in mechanical systems, analyzing wave interference at specific phase angles, and simplifying the evaluation of trigonometric equations where 120° appears. Its simplicity as a standard trigonometric value makes it a useful reference point in both educational contexts and practical calculations.