Trigonometric Ratio
Launch this tool in a distraction-free environment optimized for classroom instruction.
About
What is Trigonometric Ratio?
Trigonometric Ratio is an interactive sandbox designed to visualize the relationships between angles, coordinates, and right triangles on the Cartesian plane. By allowing students to dynamically sweep points around a circle, they can instantly see how the X (cosine) and Y (sine) legs of a right triangle stretch and shrink in response to changing angles and radii.
Mathematical Applications
This tool replaces static textbook diagrams with a manipulative environment, making the underlying concepts of trigonometry concrete and observable.
The Unit Circle & Coordinates
Set the radius to exactly 1.0 (or 100). As you rotate the point, the resulting X value precisely mirrors the Cosine of the angle, and the Y value mirrors the Sine. Students can observe in real-time why sin(90°) = 1, or why cos(180°) = -1, by looking at the physical legs of the right triangle.
Reference Angles & Quadrants
By adding multiple points, students can compare angles across different quadrants (e.g., 45°, 135°, 225°, 315°). They can visually prove that the triangles are identical in size (reference angles), but that the signs of the X and Y coordinates flip depending on which quadrant the point lives in.