Twelfth graders learn the fundamental trigonometric identities — the Pythagorean identity, reciprocal and quotient identities, and double-angle formulas — the essential toolkit for simplifying expressions and solving trig equations.
Students will be able to…
sin²θ + cos²θ always equals 1, no matter the angle. Trig identities are equations true for EVERY angle — and they’re the key to simplifying and solving. What are the essential ones?
Project this and match each trig identity to its formula — tap the identity, then tap the equation.
Tap any phase to open the teacher moves and student actions.
sin²θ + cos²θ = 1 for EVERY angle — how is that possible?
Teacher models.
Class uses Match the Identity.
Students use identities.
One identity.
Aligned to the Common Core State Standards for Mathematics (High School · Precalculus).
Prove the Pythagorean identity and use it to find sin, cos, or tan.
Prove addition and double-angle formulas.
Use inverse functions to solve trigonometric equations.
Explain how the unit circle enables trig functions.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students verify a more complex identity by transforming one side into the other using the fundamental identities. A printable trig-identities sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.