| This page shows the derivations
of the three Pythagorean Identities. A "derivation"
means that we need to create this from scratch - or, at least,
from other things that we know.
Let's start with the Unit
Circle:
Zooming in to get a better
look, we can label the sides of our right triangle...
By the Pythagorean Theorem,
we have that
Since this is a Unit Circle,
we have
Substituting, gives us
(The first Pythagorean Identity)
Most people easily remember
this first identity... But, often times, you'll need to remember
the other two when you get to Calculus.
Here's an easy way to derive
the next two, starting from the first one:
2) Divide everywhere by
Simplifying gives us the second
Pythagorean Identity...
3) Divide everywhere by
Simplifying gives us the third
and final Pythagorean Identity...
*
I always remember that the "co" guys go together!
(cotangent and cosecant)
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