Proving the Pythagorean Identities

Proving the Pythagorean Identities
Step 1: Construct axes through the given
unit circle. Let point O be the
origin and point P be a point
in the first quadrant.
Step 2: Draw
. Let be the angle
formed by
and the
positive portion of the x-axis.
Step 3: Draw the perpendicular from P
to meet the x-axis at point M.
Q1: State the ratio
in terms of
Q2: State the ratio
in terms of
Q3: Substitute the expressions you found in Q1 and Q2 into the Pythagorean Theorem to create the
first Pythagorean Identity.
Q4: Does the Pythagorean Identity hold true in the other three quadrants? Why or why not?
Q5: Show how to derive the following two forms of the Pythagorean Identity from the original
developed in Q3: