A Pythagorean Relation between Sine and Cosine

If ABC is a right triangle with right angle C, then

If we add the squares of sin A and cos A, we have:

But a2 + b2 = c2 by the Pythagorean Theorem.  Therefore (sin A)2 + (cos A)2 = 1.  In other words, the sum of the squares of the sine and cosine of the same angle will equal 1.  This is true for any angles (not just acute angles).


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