# Ch 13: Real World Trigonometric Applications

### About This Chapter

## Real World Trigonometric Applications - Chapter Summary

As you go through these lessons on real-world trigonometric applications, you will learn how to solve trigonometric equations graphically and graph the cosecant function. Steps for using the law of cosine to solve a triangle are also covered. By the end of the chapter, you should be ready to:

- Graph sine and cosine wave transformations
- Use various properties to graph cos(x)
- Transform a tangent function by making minor changes to its equation
- Identify shifted and transformed graphs
- Determine trigonometric identity using graphs
- Use the law of cosine to solve oblique triangles and real-world problems
- Prove the addition and subtraction formula for tangent

These interactive lessons provide illustrations that help you easily understand the topics presented. You can go through all of the lessons in the chapter, or just those subjects that you need to review. You can use the Help feature to submit a question to an instructor if you get stuck on a specific topic. Additionally, a brief quiz is available for each lesson to test your understanding of topics covered.

### 1. Graphing Sine and Cosine Transformations

What happens when we take the sine and cosine wave and transform them? They get bigger, smaller, faster and slower. Find out how in this lesson on sine and cosine wave transformations.

### 2. How to Graph cos(x)

The cosine function shows up often in mathematics, so being familiar with it is very useful. We will learn how to graph cos(x) using its various properties, and we'll look at how to use the graph of the sine function to create the graph of cos(x).

### 3. Graphing the Tangent Function: Amplitude, Period, Phase Shift & Vertical Shift

Take a look at how the graph of a tangent function and how we can transform it by making a few small changes to its equation. This video shows how to graph the original function and explains its transformations.

### 4. Graphing the Cosecant, Secant & Cotangent Functions

After watching this video lesson, you will learn what the graphs of the cosecant, secant, and cotangent trigonometric functions look like. You will also learn how to see if these graphs are shifted or transformed.

### 5. Using Graphs to Determine Trigonometric Identity

After watching this video lesson, you will be able to use graphs to determine whether an equation is a trigonometric identity or not. Learn what you need to look for to determine this.

### 6. Solving a Trigonometric Equation Graphically

How can you show someone that you have the right answer? This video lesson will show you how you can do this for a trigonometric equation. Learn what you need to watch for and how to get your answers.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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 BITSAT Exam - Math: Study Guide & Test Prep course

- Expressions & Reasoning in Math
- Complex Numbers & Polynomials in Algebra
- Introduction to Quadratics
- Working with Quadratic Functions Overview
- Mathematical Sequences & Series Overview
- Series & Sequences Application
- Exponential Functions & Logarithmic Equations
- Binomial Theorem Overview
- Overview of Matrices & Determinants
- Sets & Relations in Math
- Introduction to Trigonometric Functions
- Trigonometric Identities Overview
- Operating with Functions
- Solving Inequalities
- Two-Dimensional Coordinate Geometry
- Straight Lines & Angles in Coordinate Geometry
- Circular Arc & Circles in Coordinate Geometry
- Conic Sections in Coordinate Geometry
- Three-Dimensional Coordinate Geometry
- Limits & Continuity in Differential Calculus
- Calculating Derivatives
- Differentiable Functions & Min-Max Problems
- Differentiability in Integral Calculus
- Overview of Probability in Calculus
- Vectors & Scalars in Math
- Dispersion & Frequency Distributions in Statistics
- Linear Programming & Systems of Equations
- Definite Integrals
- Permutation & Combination
- Mathematical Modeling Overview
- BITSAT Exam - Math Flashcards