Trigonometry
Where trigonometry shows up in real life
14 live exhibits. Each one already works. Change a number and see what happens.
Open as board Play with these together. Solving one grows related exhibits.
Linear EquationsRoof pitch and ramp slope: rise over run
Slope is one number that decides whether a roof sheds water or a ramp is safe to roll up.
TrigonometryHow tall is that tree? Measure its shadow
One shadow and the sun’s angle give you the height, no climbing needed.
TrigonometryE6B descent planning: when to start down
A 3° path drops about 318 ft every nautical mile. Tangent turns that into a distance and a descent rate.
Ratios & ProportionsLead screw vs. ball screw: turning torque into a push
A screw trades turns for force: F = 2π × efficiency × torque ÷ lead. Friction decides whether it also holds the load with the power off.
VectorsCrossing a river: where you aim vs. where you end up
Your speed and the current add as arrows. Aim straight across and you drift; aim upstream and you can land right on target.
VectorsHanging a hammock: why the 30° rule works
Your weight and the two strap pulls are arrows that must add to zero. Hang it tight and flat, and each strap pulls with several times your weight.
VectorsCrosswind landing: splitting the wind into two parts
Pilots break the wind into “along the runway” and “across it.” That’s vector math at 60 knots.
TrigonometrySine waves: wall power and musical notes
The outlet and a tuning fork follow the same curve: amplitude, frequency, and phase.
VectorsE6B wind triangle: heading and groundspeed
Point the nose into the wind just enough to track your course. Three vectors, one triangle.
TrigonometryCrank and piston: turning rotation into back-and-forth
A crank turns a circle into a straight-line stroke. The connecting rod bends the motion away from a pure sine wave.
![The edit rotates 90°, mirrors, stretches ×0.7 sideways and ×1 up and down, slants by -0.3. As a matrix that's [0, -1; -0.7, -0.3]. Its determinant is -0.7, so areas are multiplied by 0.7 and the picture is flipped.](/snapshots/MTX-0001/1.svg)
MatricesPhoto edits are matrices: rotate, flip, stretch, and slant
Every rotate, mirror, and stretch in a photo app is four numbers. Multiply each point by them and the picture moves.
PolynomialsWhy a distortion pedal changes the sound: polynomials make harmonics
Push a pure note through a curve like x − x³/3 and new notes appear. The cube is where the extra harmonics come from.
VectorsSolar panel tilt: how much sunlight it catches
Point one arrow at the sun and one straight out of the panel. Their dot product is the share of full sunlight the panel gets.
Differential Equations & TransformsDoor closer: slam, bounce, or glide
One damping knob turns a slam into a glide. Where two dots (the poles) sit tells you which.