Identities

An identity is an equation that's true for every angle — and the most important one in trigonometry is just the Pythagorean theorem on the unit circle. This lesson collects the core trigonometric identities and shows where each comes from. We start with the Pythagorean family, then the even, odd, and cofunction symmetries that come from reflecting the unit circle. From there we build the sum and difference identities, specialize them into the double-angle and half-angle formulas, and finish with the product-to-sum and sum-to-product identities used throughout calculus and physics. In this lesson: The Pythagorean family of identities Even, odd, and cofunction symmetries Sum and difference identities Double-angle and half-angle identities Product-to-sum and sum-to-product identities This is Section 6 of Trigonometry, an 11-section chapter from The READY Academy. The full chapter playlist is linked in the description. #trigonometry #identities #mathematics #stem 00:00 Intro 00:46 The Pythagorean Family 03:55 Even, Odd, and Cofunction Symmetries 06:23 Sum and Difference Identities 10:46 Double-angle and Half-angle Identities 14:50 Product-to-sum and Sum-to-product