Small-Angle Approximations and Periodic Physical Modeling

Master radian measure, circular sector geometry, unit circle evaluations, and angular-to-linear velocity kinematics.

Analyze, graph, and evaluate reciprocal trigonometric functions and inverse trigonometric functions under restricted domains.

Construct formal algebraic proofs for fundamental, compound angle, and double angle identities, and convert linear combinations to harmonic forms.

Solve linear, quadratic-type, compound-argument, and harmonic trigonometric equations over restricted intervals and general domains.

Solve general non-right triangles using the Law of Sines, Law of Cosines, and area formulas, applying them to complex surveying, bearing, and navigational problems.

Apply Taylor small-angle approximations to physics equations and fit sinusoidal models to real-world periodic phenomena.