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Contents
Formulae
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Formulae
So far, you've seen how the trigonometric ratios are derived. You've seen how the angles and ratios are related. You've also seem some fundamental identities, largely derived from the Pythagorean Theorem. But like any mathematical concept, you wonder: how do I perform the 4 basic operations? The answers are not as simple as addition in algebra. This section on formulae intends to answer that question. You'll learn how to add angles in Addition Formulae. Multiple angles are special cases of the addition formulae. The operations on trigonometric ratios will be explained in Factor Formulae. We'll also prove all the formulae here. Actually, all the formulae can be derived from the addition formulae. Hence, we will show a geometric proof of the addition formulae, and derive the rest from there. Of course, you may take up the challenge of designing a geometric proof for each formula. These formulae are very useful for solving trigonometric equations. Do note that in a question, usually more than one formula is used. Hence, the format for this section is different from our usual style. Instead of giving examples at the end of each new concept introduced, we leave all the examples at the end. There you'll see how the different formulae are used to solve problems. Do note that all the formulae stand for both degrees and radians. Ready to take up the challenge?
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