Pre-Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Mary Jane Sterling

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Chapter 9

      Getting Started with Trig Identities

      Don’t have an identity crisis! In this chapter, you become more familiar with the possibilities for rewriting trigonometric expressions. A trig identity is really an equivalent expression or form of a function that you can use in place of the original. The equivalent format may make factoring easier, solving an application possible, and (later) performing an operation in calculus more manageable.

      The trigonometric identities are divided into many different classifications. These groupings help you remember the identities and make determining which identity to use in a particular substitution easier. In a classic trig identity problem, you try to make one side of the equation match the other side. The best way to do so is to work on just one side — the left or the right — but sometimes you need to work on both sides to see just how to work the problem to the end.

The Problems You’ll Work On

      In this chapter, you’ll work with the basic trigonometric identities in the following ways:

       Determining which trig functions are reciprocals of one another

       Creating Pythagorean identities from a right triangle whose hypotenuse measures 1 unit

       Determining the sign of identities whose angle measure is negated

       Matching up trig functions and their co-functions

       Using the periods of functions in identities

       Making the most of selected substitutions into identities

       Working on only one side of the identity

       Figuring out where to go with an identity by working both sides at once

What to Watch Out For

      Don’t let common mistakes trip you up; keep in mind that when working on trigonometric identities, some challenges will include the following:

       Keeping track of where the 1 goes in the Pythagorean identities

       Remembering the middle term when squaring binomials involving trig functions

       Correctly rewriting Pythagorean identities when solving for a squared term

       Recognizing the exponent notation

Proving Basic Trig Identities

       511–535 Prove the trig identity. Indicate your first identity substitution.

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Returning to Basic Sine and Cosine to Solve Identities

       536–540 Determine the missing term or factor in the identity by changing all functions to those using sine or cosine.

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Using Multiplication by a Conjugate to Solve Identities

       541–545 Determine