# Ch 18: Trigonometric Applications

### About This Chapter

## Trigonometric Applications - Chapter Summary and Learning Objectives

Turn your familiarity with the Pythagorean theorem into an ability to work with the law of sines and the law of cosines. In this chapter, instructors show you how they can be used to solve real-world problems by determining the length of non-right triangle sides or calculating the measures of their interior angles. By the time you finish watching the videos and taking the self-assessment quizzes included in this chapter, you should be familiar with the following:

- Applications of the law of cosines
- Applications of the law of sines
- Proofs for trigonometric addition formulas
- Proofs for trigonometric subtraction formulas

Video | Objective |
---|---|

Solving Oblique Triangles Using the Law of Cosines | Use the law of cosines to find the measure of an oblique triangle's missing side. |

Solving Real World Problems Using the Law of Cosines | Apply the law of cosines to solve sample problems based on real-world scenarios. |

Using the Law of Sines to Solve a Triangle | Find missing triangle sides or angles by applying the law of sines. |

Solving Real World Problems Using the Law of Sines | Solve practice problems that require a familiarity with the law of sines. |

Proving the Addition & Subtraction Formulas for Sine, Cosine & Tangent | Discover the postulates used to prove addition and subtraction formulas for these trigonometric functions. |

### 1. Solving Oblique Triangles Using the Law of Cosines

After watching this video lesson, you will be able to use the law of cosines to help you find a missing side or missing angle of any kind of triangle. Also, you will see what oblique triangles are.

### 2. Solving Real World Problems Using the Law of Cosines

After watching this video lesson, you will be able to use the law of cosines to solve real-world problems. Learn what kinds of real-world problems the law of cosines can help you solve.

### 3. Using the Law of Sines to Solve a Triangle

After watching this video lesson, you will be able to use the law of sines to find a missing side of a triangle as well as a missing angle of a triangle. Learn what you need to know about the triangle in order to use the formula.

### 4. Solving Real World Problems Using the Law of Sines

After watching this video lesson, you will be able to use the law of sines to solve problems that you will encounter in the real world. Learn what kind of shape you need in order to solve your real world problems.

### 5. Proving the Addition & Subtraction Formulas for Sine, Cosine & Tangent

Watch this video lesson, and you will see how the angle sum and difference identities are derived for sine, cosine, and tangent. You will also learn how you can use these identities to help you solve problems.

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### Other Chapters

Other chapters within the Precalculus: High School course

- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Graphing Piecewise Functions
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Continuity
- Limits