Whether you’re preparing for AP Calculus, Precalculus, or any math course involving trigonometry, knowing the core trigonometric identities is essential. They help you simplify expressions, prove equalities, and solve equations — and they appear on AP exams, SAT® Math, and in college-level courses.
In this guide, you’ll find every major trig identity, along with tips for remembering them and using them effectively on exams.
1. Reciprocal Identities
These express trig functions as reciprocals of each other
2. Pythagorean Identities
Derived from the Pythagorean theorem
3. Quotient Identities
Relate tangent and cotangent to sine and cosine
4. Cofunction Identities
Show relationships between complementary angles
5. Even-Odd Identities
Indicate symmetry of trig functions
6. Double-Angle Identities
7. Half-Angle Identities
8. Sum & Difference Identities
Tips for Remembering All Trig Identities
- Group them by type — Pythagorean, reciprocal, etc.
- Memorize the core — Once you know sine, cosine, and tangent rules, you can derive the rest.
- Practice regularly — Repetition through problem-solving cements recall.
