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

Chapter 9

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.

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

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

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

511.

512.

513.

514.

515.

516.

517.

518.

519.

520.

521.

522.

523.

524.

525.

526.

527.

528.

529.

530.

531.

532.

533.

534.

535.

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

536.

537.

538.

539.