Pythagorean identity
SAT glossary · Math
Definition
sin^2θ + cos^2θ = 1 — itself the Pythagorean theorem divided by the hypotenuse squared. It works for every angle, so it is a free check on any sine/cosine pair you produce.
Pythagorean identity in plain English
The Pythagorean identity, sin^2θ+cos^2θ=1, might look like a brand-new fact to memorize, but it's really just the Pythagorean theorem (a^2+b^2=c^2) in disguise — divide every term of that famous theorem by the hypotenuse squared (c^2), and you land exactly on this identity. What makes it powerful is that it holds true for absolutely EVERY angle, no exceptions — so any time you calculate a sine and cosine value for the same angle, you can plug them into this identity as an instant free check that your numbers are actually correct.
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