About This Chapter
The Unit Circle - Chapter Summary
The purpose of this chapter is to teach you how to analyze the relationships shared by the coordinate plane, circular functions and trigonometric functions associated with the unit circle. The instructor will begin with an introduction to the most widely recognized trigonometric functions, including sines, cosines and tangents. You'll also learn how sine and cosine function on the unit circle.
A key section of the lesson covers the importance of the first quadrant of the unit circle, a uniquely patterned area and the only part of the unit where angles can be used to determine the trigonometric values for all of the functions. As the lesson continues, you'll also find out how to convert between a radian, or unit of measure for an angle, and degrees. When you finish the chapter, you should:
- Have memorized the first quadrant of the unit circle, including degrees, points and radian measures
- Understand the unit circle outside of the first quadrant
- Understand the relationships between special triangles and the unit circle
- Have practiced using the unit circle
Our video lesson on the unit circle is taught by an experienced professional with an in-depth knowledge of the subject. Each brief and engaging video is composed of easy-to-understand explanations and illustrations and is supported by a lesson transcript. Additional features include links to text-based tutorials that provide more information about key concepts and terms. At the end of the chapter, you can use the video tags to revisit important parts of the lesson and take the online self-assessment quiz to see how well you understood the presentation.
1. What is Trigonometry? - Functions, Formulas & Applications
There is more to trigonometry than just sines and cosines. It can help when you need to build certain things or when you need to calculate certain distances. Learn about the usefulness of trigonometry and how triangles and circles are tied together.
2. Trigonometry: Sine and Cosine
Learn an easy trick to help you solve trigonometry problems, including problems with sine, cosine and inverse trig functions. At the end of this lesson, you'll know what SohCahToa means and how to use it.
3. 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.
4. Converting Between Radians and Degrees
Angles can be measured in degrees or radians. This lesson will explore the difference and provide you with a simple calculation that can be used to convert degrees into radians and radians into degrees.
5. Reference Angles & the Unit Circle
Watch this video lesson to learn how you can use the unit circle and its reference angles to help you solve trigonometry problems. Learn how to find your answers from the unit circle.
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Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course
- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards