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Trigonometry For Dummies, 2nd Edition by Mary Jane Sterling

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Chapter 12

Operating on Identities

In This Chapter

arrow Adding sums of angles to your identity list

arrow Subtracting angles with the difference identities

arrow Doubling angle values

arrow Taking half an angle

The basic building-block identities are the reciprocal, ratio, and Pythagorean identities, which I discuss in detail in Chapter 11. In this chapter, you take those identities a step further and develop new identities, discovering how to add, subtract, multiply, and divide the trig functions — in particular, the nice values for angles of 0, 30, 45, 60, and 90 degrees. (Those angles aren't the only ones that you can perform operations on; they're just the most convenient to use when showing how the trig identities work.) By performing such operations, you can determine the function values of even more angles than before. Whole new worlds will open up to you!

Summing It Up

The sums of angles are covered by three basic identities; these identities involve sine, cosine, and tangent. After you recognize these three identities, you can adapt them for the other three functions (cosecant, secant, and cotangent) ...

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