Unit 5 · 5 lessons

Trigonometric Identities & Equations

The identity toolkit — reciprocal, quotient, Pythagorean, compound angle and double angle formulas — and how to use it to prove identities and find every solution of a trigonometric equation on a given interval.

50 practice questions
46 flashcards
2 interactive lessons

Start lesson 1 →Unit 5 test review →

Lessons

1Basic Trigonometric IdentitiesReciprocal, quotient, Pythagorean, even/odd and cofunction identities are the vocabulary of everything that follows — and an identity is a very different object from an equation.9 questions
2Compound Angle FormulasFormulas for $sin (A \pm B)$ , $cos (A \pm B)$ and $tan (A \pm B)$ let you split unfamiliar angles like $\frac{π}{12}$ into familiar ones — and collapse long expressions back into a single ratio.10 questions
3Double Angle FormulasSetting $B = A$ in the compound angle formulas produces the double angle formulas, including three interchangeable versions of $cos 2 θ$ — and choosing the right version is most of the skill.10 questions
4Proving Identities & Solving EquationsA repeatable strategy for proving identities (work one side, never move terms across the equals sign) and for solving trigonometric equations so that you find every solution in the interval, not just the first one.Interactive10 questions
5Trig Equations with Multiple Angles and ApplicationsEquations such as $sin 2 x = c$ , $cos \frac{x}{2} = c$ and $tan 2 x = c$ : widen (or shrink) the interval, solve for the whole angle, then divide back. Plus equations that need a compound- or double-angle identity first, and equations that come from sinusoidal models.Interactive11 questions