DWG NO. 05 — Unit 5 of 10
5 online lessons · 1 in-person Review & Practice Day
Unit 4 gave sine, cosine, and their relatives concrete definitions and graphs. This unit steps back and asks a different question: which equations built from these functions are true for every angle, no matter what? Those universal equalities are identities, and they turn out to be the algebra toolkit that makes every later trig computation manageable — rewriting a messy expression, combining two angles into one, or cutting an angle in half.
The back half of the unit puts that toolkit to work solving trig equations, where — unlike an identity — the goal is to find the specific angle values that make a statement true. Expect this unit to be more symbol-dense than the last one: two of the five lessons (5.2 and 5.3) are themselves split from what would otherwise be an overloaded single lesson, and 5.4 is scoped as pure proof practice before 5.5 turns to solving.
Fundamental Identities
Reciprocal, quotient, and Pythagorean identities, and using them to simplify expressions.
→Sum and Difference Formulas
Expanding sin(A ± B), cos(A ± B), and tan(A ± B) and evaluating non-special angles exactly.
→Double-Angle and Half-Angle Formulas
Deriving double- and half-angle identities from the sum formulas and applying them.
→Proving Trigonometric Identities
Strategies for building a two-sided proof: working one side, common substitutions, and pitfalls to avoid.
→Solving Trigonometric Equations
Finding all solutions to trig equations over an interval or in general form, using identities as tools.
→Review & Practice Day 5 — bring your questions from lessons 5.1–5.5. You'll work practice problems, get feedback, and take the Unit 5 test, which also serves as this course's cumulative midterm.