Abdul's Compound Trig Fraction: A Classroom Formulation for Evaluating Nested Sine-Cosine Fractions from the Bottom Up

Continued fractions are well known in mathematics, with classical expansions for $\tan z$ dating back to Euler and Gauss. However, students at secondary school level rarely meet them in a simple, finite form using standard angles. This paper presents a novel classroom formulation: *Abdul's Compound Trig Fraction*. It is a finite nested fraction built from $\sin$ and $\cos$ of standard angles $30^{\circ}, 45^{\circ}, 60^{\circ}$, evaluated by a systematic bottom-up method.