In This Chapter
Adding sums of angles to your identity list
Subtracting angles with the difference identities
Doubling angle values
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!
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) ...