Trigonometry Review

All of trigonometry grows from a single circle of radius 1. A point travels around it, and its coordinates — cos for the horizontal reach, sin for the vertical height — generate every trig value as the angle sweeps. tan is their ratio, the slope of the radius. This 'unit circle' is the master reference: it explains why sin and cos stay between −1 and 1, why the functions repeat every 2π, and why a handful of special angles give clean, memorable values. Rebuilding the circle now sets up everything in the journeyman tier.