Name: Period: Date: 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:
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