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Pre-Calculus For Dummies, 2nd Edition by Elleyne Kase, Yang Kuang PhD

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Chapter 9

Advanced Identities: Your Keys to Pre-Calc Success

In This Chapter

arrow Applying the sum and difference formulas of trig functions

arrow Utilizing double-angle formulas

arrow Cutting angles in two with half-angle formulas

arrow Changing from products to sums and back

arrow Tossing aside exponents with power-reducing formulas

Prior to the invention of calculators (not as long ago as you may imagine), people had only one way to calculate the exact trig values for angles not shown on the unit circle: using advanced identities. Even now, most calculators give you only an approximation of the trig value, not the exact one. Exact values are important to trig calculations and to their applications (and to teachers, of course). Engineers designing a bridge, for example, don’t want an almost correct value — and neither should you, for that matter.

This chapter is the meat and potatoes of pre-calc identities: It contains the bulk of the formulas that you need to know for calculus. It builds on the basic identities ...

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