Right triangles, the unit circle, identities, inverses, and polar coordinates.
The foundational concepts of trigonometry: angles and their measures, angle relationships and similar triangles, the definitions of the six trigonometric functions, quadrantal angles, and the basic (reciprocal, quotient, and Pythagorean) identities.
Trigonometric functions defined through right triangles: acute and non-acute angles, reference angles, approximating function values, significant digits, and applications involving angles of elevation and depression, bearing, distance, and height.
Radian measure and the circular-function view of trigonometry: converting between degrees and radians, arc length and the area of a sector, the unit circle and the values of the circular functions, and linear and angular speed.
Graphing the six trigonometric functions: amplitude, period, and phase shifts of sine and cosine; translations; and the graphs of tangent, cotangent, secant, and cosecant.
Working with trigonometric identities: the fundamental identities, verifying identities, the sum and difference identities, and the double-angle, product-to-sum, and half-angle identities.
The inverse trigonometric functions and their graphs, and solving trigonometric equations by linear and quadratic methods, with multiple and half angles, and with inverse trigonometric functions.
Solving oblique triangles with the Law of Sines (including the ambiguous case) and the Law of Cosines (with Heron’s formula for area), and an introduction to vectors: geometric and algebraic representations, applications, and the dot product.
The trigonometric (polar) form of complex numbers: a review of imaginary numbers, polar form, the product and quotient theorems, De Moivre’s Theorem for powers and roots, and polar coordinate systems and graphing.