The Unit Circle and Trigonometric Functions: Math Unit 4, Grade 12 (Letters & Devotion)

Description

The Unit Circle and Trigonometric Functions is Unit 4 of Precalculus: Functions, Trigonometry, and Mathematical Modeling (Grade 12), the Letters & Devotion Math course, complete in one printable PDF: 11 lessons, the unit check-up and the answer key, 82 pages.

• Radian measure as arc length on the unit circle
• Exact trigonometric values at special unit circle angles
• The equivalence and extension of right-triangle trig to unit-circle trig
• Reference angles and quadrant sign patterns on the unit circle
• The sine and cosine graphs as traces of the unit circle’s y- and x-coordinates over rotation
• Amplitude, period, phase shift, and midline transformations of sine and cosine
• The tangent function’s period and asymptotes derived from sin θ / cos θ
• Inverse trigonometric functions defined via domain restriction
• Periodic real-world phenomena modeled by sine or cosine functions
• The structural fit between a candidate function family and a novel periodic or non-periodic dataset
• Unit-circle symmetry relationships for supplementary and related angles

Every lesson is written for a parent with no teaching background: it opens with a short script to read aloud, names the specific wrong idea a student is likely to reach for and how to correct it, and closes with a practice sheet you may copy for your household. Scripture references are King James Version throughout. Black-and-white, 8.5 x 11 in. The whole year of this course is also in this store as a single book.

AI note: The written content of this resource was drafted with AI tools, then reviewed and edited by the author.