The Complements Theorem

In this post, we discuss the proof behind one of the most commonly used identities in trigonometry. We examine the equations below and  show why the relationships always hold. To students who have taken trigonometry, I’m sure that you have met these equation before.  The proof of these equations are as follows. Consider triangle right […]
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Pythagorean Theorem, Distance Formula, and Equation of a Circle

In my Algebraic and Geometric Proof of the Pythagorean Theorem post, we have learned that a right triangle with side lengths and and hypotenuse length , the sum of the squares of and is equal to the square of . Placing it in equation form we have . If we place the triangle in the […]
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The Algebraic and Geometric Proofs of Pythagorean Theorem

The Pythagorean Theorem states that if a right triangle has side lengths and , where is the hypotenuse, then the sum of the squares of the two shorter lengths is equal to the square of the length of its hypotenuse. Putting it in equation form, we have: . For example, if a right triangle has […]
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