Chapter 3: Trigonometric Identities and Equations

Difficulty Level: At Grade Created by: CK-12

Chapter Outline

Chapter Summary

Here are the identities studied in this chapter:

Quotient & Reciprocal Identities

Pythagorean Identities

Even & Odd Identities

Co-Function Identities

Sum and Difference Identities

Double Angle Identities

Half Angle Identities

Product to Sum & Sum to Product Identities

Linear Combination Formula

, where and

Review Questions

1. Find the sine, cosine, and tangent of an angle with terminal side on .
2. If and , find .
3. Simplify: .
4. Verify the identity:

For problems 5-8, find all the solutions in the interval .

1. Solve the trigonometric equation over the interval .
2. Solve the trigonometric equation over the interval .
3. Solve the trigonometric equation for all real values of .

Find the exact value of:

1. Write as a product:
2. Simplify:
3. Simplify:
4. Derive a formula for .
5. If you solve for , you would get . This new formula is used to reduce powers of cosine by substituting in the right part of the equation for . Try writing in terms of the first power of cosine.
6. If you solve for , you would get . Similar to the new formula above, this one is used to reduce powers of sine. Try writing in terms of the first power of cosine.
7. Rewrite in terms of the first power of cosine:

Texas Instruments Resources

In the CK-12 Texas Instruments Trigonometry FlexBook® resource, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9701.

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