Find tan from sin: Interactive Geometric Demonstration

This GeoGebra example demonstrates how to derive the tangent (tan) of an angle from its given sine (sin) value using a unit circle and right-triangle construction. The core mathematical concept is the trigonometric identity tan = sin/cos, where cos is obtained from the Pythagorean relation on the unit circle. The construction uses commands such as Point, Circle, Intersect, OrthogonalLine, Vector, SurdText, Textfield, and InputBox1 to create an interactive environment: a unit circle, a movable point defining the angle, perpendicular lines forming a right triangle, and an input box where users can enter a sine value, causing the diagram and computed tangent to update dynamically. This is ideal for high school trigonometry lessons, helping students visualize the relationship between sine, cosine, and tangent, and for college preparatory review of trigonometric ratios.