Trigonometry
The mathematics of triangles and circles. Starting from ratios of sides in a right triangle, trigonometry generalizes through the unit circle into the language of waves, oscillations, and rotations — the language in which physics describes everything that repeats.
Angles & Radians
Two ways to measure rotation. Degrees feel familiar; radians are what calculus prefers and why.
Sine, Cosine & Tangent
Three ratios of the sides of a right triangle. SOH-CAH-TOA and what each function really measures.
Law of Sines & Cosines
Solving triangles that aren't right-angled. The general extensions of the Pythagorean theorem.
The Unit Circle
The single picture that organizes all of trigonometry. Coordinates of a point on a unit-radius circle, indexed by angle.
Graphs of Trig Functions
Sine and cosine as periodic curves. Amplitude, period, phase, and the building blocks of every wave.
Trigonometric Identities
The algebra of trig functions. Pythagorean, angle-sum, and double-angle identities — and where they come from.
Inverse Trigonometric Functions
arcsin, arccos, arctan and friends. Why we restrict domains, principal values, and the composition trap.
Trigonometric Equations
Solving sin x = k and harder. General solutions with +2πk, identity reduction, factoring, and extraneous roots from squaring.
Polar Coordinates
Points as (r, θ) instead of (x, y). Conversion both ways, polar equations of circles and roses, and a teaser for complex numbers.
Vectors in Two Dimensions
Arrows with magnitude and direction. Decompose into components with cos/sin, reassemble with Pythagoras and atan2, and add componentwise.