Trigonometry & Geometry Mind Map

Every trigonometry & geometry visualization on this site on one map. The branches are the main ideas. Each leaf is a page; the grey line under it is the one thing to remember about it. Click a branch to focus on it, click a page to open it.

Recall mode hides the page names. Read the hint, say the name, then click the "?" to check.

1. How the map is organized

Overview of the trigonometry & geometry mind map: Geometry proofs, Unit circle and graphs, Waves, Polar curves, Parametric curves, Conic sections, Triangle trigonometry. — The map at a glance: 7 branches, 31 pages.

Look at how the picture is made and you know its branch:

Is it a fact about fixed shapes? Triangles, circles and graphs proved by moving pieces: geometry proofs.
Is it sin, cos or tan of one angle? The unit circle branch; if the sine moves through a medium over time, it is waves.
How is the curve drawn? A radius for each angle is a polar curve; x(t) and y(t) together are a parametric curve; a degree-2 equation in x and y is a conic.

2. The branches side by side

Branch	Described by	Key number	Example
Geometry proofs	lengths, angles, counts	a fixed sum or ratio	a² + b² = c²
Unit circle and graphs	y = a·sin(bx + c) + d	period 2π/\|b\|	sin² θ + cos² θ = 1
Waves	y = A sin(kx − ωt)	speed v = fλ	standing wave nodes
Polar curves	r = f(θ)	petals, symmetry	r = cos 3θ
Parametric curves	x(t), y(t)	frequency ratio	Lissajous 3:2
Conic sections	Ax² + Bxy + Cy² + … = 0	eccentricity e	ellipse e < 1

3. Five facts to remember

On the unit circle cos θ is the x and sin θ the y of the point, so sin² θ + cos² θ = 1.
A radian is the angle whose arc equals the radius; a full turn is 2π.
In y = a·sin(bx + c) + d the period is 2π/|b| and the phase shift is −c/b.
Waves add: crest on crest doubles the height, crest on trough cancels it.
Every conic has |PF| = e·|PD|: the eccentricity e alone decides ellipse, parabola or hyperbola.

See all trigonometry & geometry pages in the index, or the other mind maps.