Unit Circle

Showing the Relationship between Angles and Trigonometric Functions

Unit Circle shows the relationship between angles and trigonometric functions like sine and cosine. To do this, the program implements an interactive "unit circle" (radius = 1) diagram, where the user can click or drag to set angles and see how the values of trigonometric functions change accordingly.

So... what is a Unit Circle?

The unit circle (where the radius equals 1) provides a very clear demonstration of how various trigonometric functions relate to angles and one another. Draw an angle line from the origin to a point on the circumphrence of the circle; the (x,y) coordinates of that point will will be the cosine and sine of the angle.

In Unit Circle, use the mouse to set the angle line by either clicking or dragging the pointer inside the diagram. Or, change the trigonmetric values in the fields, and the angle will automatically adjust.

The inspiration for this program was provided by my home-schooled daughters, who had difficulty understanding the nature of trigonometry. As an educational tool, Unit Circle has been a success, and it may evolve into a larger application for exploring other aspects of trigonometry and geometry.

Programming Notes

The program isn't rocket science, but did provide an opportunity to work with the Cairo graphics library used in the latest versions of the GTK+ toolkit. If you look in Unit Circle's src/callbacks.c file, you'll see how I used Cairo to draw the diagram and reflect mouse operations.

I haven't time at the moment to write a full Cairo tutorial, though if enough people ask, I may consider working on it.