The Pythagorean Identities are what I consider to be the second pillar of the trigonometric identities. With the combination of these identities and the sum identities, almost any other identity can be derived.
Students don't always understand what having an identity actually means. A teacher, Sheldon P. Gordon, decided that his trigonometry students didn't understand the concept of an identity. He decided to show them. He asked students to graph the Pythagorean identity sin^2(x)+cos^2(x) in their graphing calculators. The result was a flat line, y=1. That took the students by surprise. Mr. Gordan said, "The result, a horizontal line, made a dramatic impact on the students about the significance of what an identity actually is --in this example, an equation that holds for every value of x." Next, Mr. Gordon had his students graph sin^3+cos^3 and sin^4+cos^4 in their calculators. Most students were expecting some sort of line like they got before, but that is not what they saw. This helped the students see that an identity is something that holds for all values, and not any equation can be an identity.
Below is an applet that helps students see they Pythagorean Identities in another geometric way that may also help students see the concept of an identity.