Prentice Hall Algebra 2

Practice and Problem-Solving Exercises

A Practice

Use an angle sum identity to derive each double-angle identity. A See Problems 1, 2, and 3.

  1. sine 2 theta equals 2 sine theta cosine theta
  2. tangent 2 theta equals . fraction 2 tangent theta , over 1 minus , tangent squared , theta end fraction

Use a double-angle identity to find the exact value of each expression.

  1. sine , 240 degrees
  2. cosine , 120 degrees
  3. tangent , 120 degrees
  4. sine , 90 degrees
  5. cosine , 240 degrees
  6. tangent , 240 degrees
  7. cosine , 600 degrees
  8. sine , 600 degrees

Use a half-angle identity to find the exact value of each expression. A See Problems 4.

  1. cosine , 15 degrees
  2. tangent , 15 degrees
  3. sine , 15 degrees
  4. sine 22 . 5 degrees
  5. cosine , 22 . 5 degrees
  6. tan 22 . 5 degrees
  7. cosine , 90 degrees
  8. sine 7 . 5 degrees

Given cosine theta equals negative , 4 fifths and 90 degrees less than theta less than 180 degrees comma find the exact value of each expression. See Problem 5.

  1. sine , theta over 2
  2. cosine , theta over 2
  3. tangent , theta over 2
  4. co-tangent , theta over 2

Given cosine theta equals negative , 15 over 17 and 180 degrees less than theta less than 270 degrees comma find the exact value of each expression.

  1. sine , theta over 2
  2. cosine , theta over 2
  3. tangent , theta over 2
  4. secant , theta over 2

B Apply

  1. Think About a Plan Triangle ABC is a right triangle with right angle C. Show that cosine squared . b over 2 , equals . fraction eh plus c , over 2 c end fraction . .

    • What identity will you use?
    • How can you find the ratio or ratios you need to substitute in the identity?
    • What will be your last step in the solution?

      Right triangle A B C with standard side lengths and the right angle at C.


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Table of Contents

Prentice Hall Algebra 2 Chapter 1 Expressions, Equations, and Inequalities Chapter 2 Functions, Equations, and Graphs Chapter 3 Linear Systems Chapter 4 Quadratic Functions and Equations Chapter 5 Polynomials and Polynomial Functions Chapter 6 Radical Functions and Rational Exponents Chapter 7 Exponential and Logarithmic Functions Chapter 8 Rational Functions Chapter 9 Sequences and Series Chapter 10 Quadratic Relations and Conic Sections Chapter 11 Probability and Statistics Chapter 12 Matrices Chapter 13 Periodic Functions and Trigonometry Chapter 14 Trigonometric Identities and Equations Skills Handbook English/Spanish Illustrated Glossary Selected Answers Index Acknowledgments