Trigger
Touchable Trigonometry

Trigger features a dynamic, touchable "Complete Triangle" figure, whose segment lengths represent the values of the six trigonometric functions of an angle (and 1 the radius of the unit circle, about which the figure is built).

Many properties of the Complete Triangle figure are detailed in the document —"(Almost) Everything You Need to Remember about Trigonometry, in One Simple Diagram"— linked at right. By adding an element of motion, Trigger improves the educational impact of the Complete Triangle concept.

Trigger's purpose is to be "educationally illustrative" rather than "comprehensively computational". It is not an arbitrary-precision trigonometric computing machine, but an innovative learning aid.

The Main View

Trigger's window is dominated by a circular area that displays the Complete Triangle figure. Swiping a finger around in that area changes figure's defining angle, and thus also its shape. The top-left corner of the window shows the angle's measure, in degrees, radians, and "piece of pi" format (which expresses the radian measure as a multiple of pi).

Along the top of the window are the values of the six trigonometric functions associated with the Complete Triangle's defining angle. The values are color-coded to match segments in the figure, to underscore the key connection: each trig value is just the length of a segment (with a possible change of sign). Even the radian measure of the angle appears in the figure as the length of a circular arc!

As the Complete Triangle's angle changes, its segments change, sometimes shrinking to points (having "zero length") and sometimes extending into endless rays (having "infinite length"). Continued use of Trigger promotes an intuitive understanding of how these segments (and the trig values) behave.

Calculators

Trigger provides a pair of handy calculators to explore numerical properties of the trig values.

Easily-configurable using "picker wheels", the calculators compute formulas involving trig values. Use them to verify common trig identities: for instance, a calculator set to compute  sin2 + cos2  will dutifully yield the value  1.000,  no matter how wildy you swipe your finger around Complete Triangle display, thus demonstrating that the value of the trig expression doesn't depend upon the value of any particular angle. (Importantly, the geometry of the Complete Triangle figure explains why this is so.)

By providing two calculators, Trigger allows for consideration of more complex identities, such as  |tan| + |cot| = |sec| × |csc|;  simply set one calculator to compute the left-hand side of the equation, set the other calculator to compute the right-hand side, and marvel as the computed values always match.

More Options

In addition to the ability to switch between displaying trig values or calculators, Trigger offers the following:

Exact special values. With this option on, Trigger displays trig values in exact algebraic form when the figure's angle is 0°, 30°, 45°, 60°, 90°, or a like angle in any quadrant.

Angle steps. These settings round the figure's angle to the nearest 1, 5, or 15 degrees, making it easier to swipe around the circle and hit a desired mark.

"Swiping affects" setting. Initially, Trigger adjusts the figure's angle based on the position of one's finger in the display. Use this setting so that the figure's "sine segment" (or cosine segment, or ...) tracks the finger position.

Quadrant Zoom. Double-tap a quadrant to zoom in on it. (The figure above shows a zoom into Quadrant IV.) When zoomed, angles and values are restricted to the selected quadrant. (A consequence of this is that values —such as tan— which may be undefined in a full-circle context become well-defined, but infinite.)

Sine-and-Cosine-only Zoom. Double-tap the center of the display to zoom in on the unit circle. In this mode, all segments (and trig values) except for sine and cosine disappear.

Supplementary Trig PDF. Through Trigger's info panel, you can download and view the document "(Almost) Everything You Need to Remember about Trig, in One Simple Diagram", which surveys in great detail the information found in the Complete Triangle figure. This PDF is also available via the link at the top of this page.

Tricochet, the triple-ricochet design, Trigger, and Tri are trademarks of BDS McConnell. iPhone and iPod touch are trademarks of Apple, Inc.