Fun Trig

Fun Trig is a simple native app for the iPhone that uses animation to help K-12 Pre-Calculus students to explore The Unit Circle and understand Circle Trigonometry better in order to visualize the meaning of the 'sine wave' which is so important in describing many different natural phenomena. The sine and cosine of an angle are defined as the lengths of the y (orange) and x (green) coordinates of a point rotating counterclockwise around a circle of radius one (Unit Circle) centered at the origin. When you click on the Graphs button you can watch the sine (orange) and cosine (green) graphs in a separate screen, where the mapping between the coordinates of a point on the unit circle and the distance travelled around it (yellow) can be watched through the animation.

By using the app and its features (like visualizing the angle of reference for any given angle), students might just 'watch' the answers to some usual questions they might be required to answer while learning Trigonometry such as:

  • What is the largest value of the sine function? What is the smallest value?
  • Does the sine of an angle increase or decrease as the angle increases from 180° to 270°?
  • Find all values of an angle between 0° and 360° such that its sine is equal to -0.8192
  • TWhat is the reference angle of 238°

For simplicity only sine and cosine are drawn. Tap on the screen to pause/resume the animation.

Why Fun Trig?

Prior to move to Software Engineering, for a number of years back in the 80s, I worked as a Calculus and Pascal professor for the well-known Massachusetts Prep School Phillips Andover Academy ( My first apps for the Macintosh in the mid-eighties were in fact Math educational software and also applications for the Science Museum of Barcelona. This little free app is a way to remember those very happy days of my professional life. To my surprise, the number of downloads of the app so far seems to have justified the effort!