# Ch 24: Trigonometry: NBPTS Math - Adolescence & Young Adult

### About This Chapter

## Trigonometry: NBPTS Math - Adolescence & Young Adult - Chapter Summary

Our expert instructors deliver these lessons as short videos that act as refreshers for the NBPTS Math test. When you are done with this chapter, you will be better-prepared to answer trigonometry-related NBPTS test questions on such lesson topics as:

- Getting familiar with the definition, uses, converse and special cases of the Pythagorean Theorem
- Finding out about trigonometry and the Pythagorean Theorem
- Solving a triangle using sines
- Knowing how to use radian measure
- Learning how to use unit circles
- Understanding the graphing of sine, cosine, tangent, cotangent, transformations, secant, and cosecant functions
- The verification and use of trigonometric identities
- Applying the identities of sum and difference

Videos run for 5-10 minutes and come with a short self-assessment quiz. If you need to go over the material again, look to the provided transcripts or use the keyword-based timeline tool that takes you to an exact section of a video. You can also ask questions of the expert instructors.

### 1. Pythagorean Theorem: Definition & Example

Learn what the Pythagorean Theorem says about a right triangle and the relationships of its three sides to each other by watching this video lesson. Also learn how you can use this to your advantage when solving problems.

### 2. The Pythagorean Theorem: Practice and Application

The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.

### 3. The Pythagorean Theorem: Converse and Special Cases

The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.

### 4. Trigonometry and the Pythagorean Theorem

Explore how the Pythagorean Theorem can be used in conjunction with trigonometric functions. In this lesson, take an inverse trigonometric function, and define all three sides of a right triangle.

### 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. Radian Measure: Definition & Formula

In mathematics, the radian is the standard unit of angular measure. This lesson will define radian and work through some problems involving radians. The lesson will end with a quiz.

### 7. Using Unit Circles to Relate Right Triangles to Sine & Cosine

The unit circle is a helpful tool for understanding trigonometric concepts. In this lesson, we'll look at right triangles on the unit circle to better grasp sine and cosine.

### 8. Unit Circle: Memorizing the First Quadrant

Memorizing the unit circle can be a daunting task, but this lesson will show you a pattern to help you memorize the points, degree measures, and radian measures for the entire first quadrant.

### 9. Graphing Sine and Cosine

Sine and cosine aren't just for triangles; they can also be waves. See them graphed on the unit circle and then learn how that translates into the sine and cosine waves.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. Trigonometric Identities: Definition & Uses

After watching this video lesson, you will understand what a trigonometric identity is. You will also know the different kinds of identities you will come across.

### 14. Verifying Trigonometric Identities with Unit Circles

In this lesson, we will review the unit circle and the corresponding definitions of the trigonometric functions. We will then verify several trigonometric identities using the unit circle.

### 15. Applying the Sum & Difference Identities

Watch this video lesson to learn the six sum and difference identities for the trig functions of sine, cosine, and tangent. Also, learn how you can use them to your advantage when solving tough trig problems.

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### Other Chapters

Other chapters within the National Board Certification Exam - Mathematics/Adolescence & Young Adulthood: Practice & Study Guide course

- Teaching Math: NBPTS Math - Adolescence & Young Adult
- Understanding Math: NBPTS Math - Adolescence & Young Adult
- Numbers: NBPTS Math - Adolescence & Young Adult
- Operations: NBPTS Math - Adolescence & Young Adult
- Algebraic Reasoning: NBPTS Math - Adolescence & Young Adult
- Equations: NBPTS Math - Adolescence & Young Adult
- Systems of Equations: NBPTS Math - Adolescence & Young Adult
- Inequalities: NBPTS Math - Adolescence & Young Adult
- Functions: NBPTS Math - Adolescence & Young Adult
- Exponents & Exponential Functions: NBPTS Math - Adolescence & Young Adult
- Logarithmic Functions: NBPTS Math - Adolescence & Young Adult
- Rational Functions: NBPTS Math - Adolescence & Young Adult
- Quadratic Functions: NBPTS Math - Adolescence & Young Adult
- Trigonometric Functions: NBPTS Math - Adolescence & Young Adult
- Polynomials: NBPTS Math - Adolescence & Young Adult
- Series & Sequences: NBPTS Math - Adolescence & Young Adult
- Geometry Concepts: NBPTS Math - Adolescence & Young Adult
- Lines: NBPTS Math - Adolescence & Young Adult
- Angles: NBPTS Math - Adolescence & Young Adult
- Transformations: NBPTS Math - Adolescence & Young Adult
- Congruence & Similarity: NBPTS Math - Adolescence & Young Adult
- Circles: NBPTS Math - Adolescence & Young Adult
- Area & Volume: NBPTS Math - Adolescence & Young Adult
- Discrete Mathematics: NBPTS Math - Adolescence & Young Adult
- Data Analysis & Statistics: NBPTS Math - Adolescence & Young Adult
- Probability: NBPTS Math - Adolescence & Young Adult
- Calculus: NBPTS Math - Adolescence & Young Adult
- Student Development: NBPTS Math - Adolescence & Young Adult
- Practice of Teaching: NBPTS Math - Adolescence & Young Adult
- Learning Environments: NBPTS Math - Adolescence & Young Adult
- Thinking Mathematically: NBPTS Math - Adolescence & Young Adult
- Assessment: NBPTS Math - Adolescence & Young Adult
- Reflection & Growth: NBPTS Math - Adolescence & Young Adult
- Families & Communities: NBPTS Math - Adolescence & Young Adult
- Professional Community: NBPTS Math - Adolescence & Young Adult
- National Board Certification Exam - Mathematics/Adolescence & Young Adulthood Flashcards