# Ch 17: NYSTCE Mathematics: Applications of Trigonometry

### About This Chapter

## NYSTCE Mathematics: Applications of Trigonometry - Chapter Summary

Unlike sailing through the famous triangle that has supposedly swallowed up aircraft and ships over the centuries, you can explore these triangles without the fear that you will get lost and never be seen again. These video lessons can function as your life preserver as you get set to take the NYSTCE Mathematics exam. They will illustrate the following material:

- Trigonometric ratios and related practice problems
- Understanding and finding sine, cosine and tangent
- How to find the area of a triangle
- Defining and using the laws of sines and cosines
- Applying the laws of sines and cosines in the real world
- Understanding sinusoidal function and simple harmonic motion
- Finding solutions to trigonometric equations and more
- Representing a wave using the sinusoidal function

This study guide contains features that are designed to enable you to make the most of your study time. The timeline gives you the option of skipping through material you don't want to review and going directly to new or less familiar parts of a lesson. Further, you can play back sections of any lesson without having to re-watch the entire video, and we have embedded links in the quizzes that will take you to specific points in the lesson quickly and easily.

### 1. Trigonometric Ratios and Similarity

Where do terms like sine, cosine and tangent come from? In this lesson, we'll learn about how similarity with right triangles leads to trigonometric ratios.

### 2. Practice Finding the Trigonometric Ratios

So you know what sine, cosine and tangent are. Great! But how do you use them? Find out how in this lesson as we find missing sides and angles using trigonometric ratios.

### 3. Using Sine to Find the Area of a Triangle

Since you first started working with triangles in math class, chances are you've been exposed to the formula for the area of a triangle. However, that is only good if you know the height of the triangle. This lesson shows you how to get around that.

### 4. Law of Sines: Definition and Application

Don't get stuck trying to find missing sides or angles in a triangle. Use the Law of Sines to rescue you from any perilous triangle in which you have just a few pieces of information.

### 5. 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.

### 6. 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.

### 7. Law of Cosines: Definition and Application

In this lesson, we'll learn how to solve problems involving three sides and one angle in a triangle. The Law of Cosines, a modification of the Pythagorean Theorem, will save the day.

### 8. 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.

### 9. 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.

### 10. The Sinusoidal Description of Simple Harmonic Motion

Watch this video to learn about simple harmonic motion. Learn the sinusoidal equations we use to solve problems of simple harmonic motion, and test your knowledge afterwards with a short quiz.

### 11. 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.

### 12. How to Solve Trigonometric Equations for X

Adding trigonometric functions into standard algebra equations adds complexity. Learn how to solve trigonometric equations for x and how to use inverse operations to simplify equations.

### 13. Solving Trigonometric Equations with Restricted Domains

After watching this video lesson, you will be able to find the right answer for a trigonometric equation with a restricted domain. Learn what it means to have a restricted domain and what you need to do to find your answer.

### 14. Solving Trigonometric Equations with Infinite Solutions

Watch this video lesson and you will learn that all trigonometric equations have an infinite set of solutions. But you will also see that we can still go ahead and solve our equations and find concrete answers.

### 15. Finding the Sinusoidal Function

After watching this video lesson, you will be able to write a sinusoidal function to represent any wave that you see. Learn what parts of the function make the wave shift up, down, to the left, and to the right.

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### Other Chapters

Other chapters within the NYSTCE Mathematics (004): Practice & Study Guide course

- NYSTCE Mathematics: Fractions, Decimals & Percents
- NYSTCE Mathematics: Complex Numbers
- NYSTCE Mathematics: Factoring & Divisibility
- NYSTCE Mathematics: Exponents
- NYSTCE Mathematics: Patterns & Functions
- NYSTCE Mathematics: Understanding Algebraic Expressions
- NYSTCE Mathematics: Solving Algebraic Equations
- NYSTCE Mathematics: Linear Equations
- NYSTCE Mathematics: Quadratic Functions
- NYSTCE Mathematics: Polynomial Functions
- NYSTCE Mathematics: Exponential Expressions
- NYSTCE Mathematics: Absolute Value Expressions
- NYSTCE Mathematics: Rational Expressions
- NYSTCE Mathematics: Radical Expressions
- NYSTCE Mathematics: Exponential & Logarithmic Functions
- NYSTCE Mathematics: Trigonometry
- NYSTCE Mathematics: Calculus Concepts
- NYSTCE Mathematics: Calculus Applications
- NYSTCE Mathematics: Principles of Measurement
- NYSTCE Mathematics: Lines & Angles
- NYSTCE Mathematics: Parallel Lines & Symmetry
- NYSTCE Mathematics: Geometric Construction
- NYSTCE Mathematics: Geometric Shapes
- NYSTCE Mathematics: Triangle Proofs & Theorems
- NYSTCE Mathematics: Geometric Solids
- NYSTCE Mathematics: Conic Sections
- NYSTCE Mathematics: Vector Operations
- NYSTCE Mathematics: Transformations in Geometry
- NYSTCE Mathematics: Coordinate Geometry
- NYSTCE Mathematics: Sequences & Series
- NYSTCE Mathematics: Counting Strategies
- NYSTCE Mathematics: Probability
- NYSTCE Mathematics: Probability Distributions
- NYSTCE Mathematics: Data Analysis & Statistics
- NYSTCE Mathematics: Sampling & Prediction
- NYSTCE Mathematics: Regression & Correlation
- NYSTCE Mathematics: Discrete Mathematics
- NYSTCE Mathematics Flashcards