Trigger features a dynamic, touch-friendly “Complete Triangle” figure, which is, quite simply, the single greatest teaching tool for trigonometry.

Representing the six trig functions as geometric segments, the Triangle fosters real, *intuitive* understanding of the behaviors of, and relationships among, those functions. Trigger‘s interactivity compounds these benefits visually, and its calculators allow for exploring numerically.

The Complete Triangle figure dominates Trigger’s screen. Swiping changes the figure’s defining angle*, and thus also its shape.

Sometimes, some segments shrink to mere points; other times, some segments extend into endless rays. The corresponding trig values —the *lengths* of those segments— range from zero to infinity. Just a few moments with Trigger explains how —and, more-importantly, *why*— the segments and values behave as they do.

Trigger’s top-left corner shows the Triangle’s defining angle measure, in degrees, in radians, and in “piece of pi” format (which expresses the radian measure as a multiple of pi).

Trigger optionally displays the radian measure as a fraction of tau (aka, 2 pi).

* Press-and-hold a trig value in order to make swipes affect a particular segment’s length, instead of the angle.

Trigger also provides a pair of calculators to explore numerical trigonometric properties.

Easily-configurable (just press-and-hold), the calculators evaluate simple formulas. Use them, for instance, to verify common trig identities:

This calculator unwaveringly computes the value

**1.000**.

The values of these calculators vary, but **they always match**.

Of course, the geometry of the Complete Triangle explains these facts nicely.

A handy, retractable ribbon offers these options:

Trig values vs. Calculators.

(In)Exact values at 0°, 30°, 45°, 60°, 90°.

1° vs. 5° precision for circular swipes.

Radians in π (3.14...) vs. τ (6.28...).

One of the first 500 apps available in the App Store on Day One*, Trigger —now, Trigger *2*— has been re-written, re-designed, and completely *re-jiggered* for modern iOS devices, bringing the Complete Triangle to the next generation of trig enthusiasts.

* Does anyone remember iPhone OS 2?

Enjoy!