Çözüldü Geometry - Trigonometry - Similar Triangles

In a semicircle, a rectangle is inscribed with a 1-unit-long side perpendicular to the diameter; what is the trigonometric function of the rectangle's diagonal in terms of the angle formed by the line connecting the midpoint of this side to the center of the semicircle?

The distance from the mid-point of the side to the diameter: a = 0.5 unit
The angle: θ
The distance from the mid-point to the semi-circle's center: b = a·csc(θ) units
The length of the diagonal: D
Applying Thales's Theorem to the similar triangles a / b = 2a / D ⇒ D = 2b = 2a·csc(θ) = 2·(1 / 2)·csc(θ) = csc(θ).

Note: Drawing is homework for the interested students.