Ch 23: Algebra II: Trigonometry Overview
About This Chapter
Algebra II: Trigonometry Overview - Chapter Summary
High school students need to read and understand a great deal of information both before they graduate and as they move on in college or the professional world. This chapter provides students with focused training on developing their knowledge of trigonometry.
Instead of an endless chapter of information, the chapter has been divided into short, individualized lessons. Students have the option to review all of the lessons in order, but they can also pick and choose lesson topics in which they need the most assistance. The chapter menu provides a list of all lessons available, and since each lesson is only focused on a single topic, students can easily find what they need. After completing this chapter, students will be ready to:
- Graph sine and cosine transformations and the tangent function
- Memorize the first quadrant of the unit circle
- Use unit circles to relate right triangles to sine and cosine
- Explain the types of special right triangles and their properties
- Apply the double angle formula
- Convert radians to degrees and vice versa
- Solve trigonometric equations for X
1. Graphing Sine and Cosine Transformations
The sine and cosine signal waveforms, or waves, can be transformed in multiple ways. Learn how to identify the three types of sine and cosine transformations, including amplitude, period, and phase shift, and practice graphing the transformations with sample problems.
2. Graphing the Tangent Function: Amplitude, Period, Phase Shift & Vertical Shift
Unlike other trigonometric functions, a tangent function can be transformed in four different ways. Learn how to graph the tangent function and to visualize and change the amplitude, period, phase shift, and vertical shift of a tangent function.
3. Unit Circle: Memorizing the First Quadrant
Memorizing the unit circle allows for calculation of its angles' trigonometric values without a calculator. Explore and memorize the unit circle's first quadrant, including its main points, and its sine, cosine, and tangent values.
4. Using Unit Circles to Relate Right Triangles to Sine & Cosine
A unit circle is a circle with a radius of 1, and a right triangle is a triangle with one right angle. Learn the trigonometric properties of right triangles and how to use unit circles to relate right triangles to sine and cosine.
5. Special Right Triangles: Types and Properties
There are two types of special right triangles that have either 30-60-90 degree angles or 45-45-90 degree angles. Learn more about the definitions and explore the properties of 30-60-90 and 45-45-90 degree angles of special right triangles through examples.
6. The Double Angle Formula
In trigonometry, a double angle is twice as large as a common angle. Learn how to calculate the double angle formula, explore trigonometry twins for sine, cosine, and tangent, and apply this information in practice problems using the double angle formula.
7. Converting Between Radians and Degrees
The two most widely used units of measure for angles are degrees and radians. Learn how to convert radians to degrees and degrees to radians using the concepts of proportion and priority.
8. How to Solve Trigonometric Equations for X
Trigonometric functions can be simplified using their inverses and their angles can be solved within their restricted domains. Learn how to solve trigonometric equations for x using inverse operations and based on trigonometric restrictions.
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Other Chapters
Other chapters within the High School Algebra II: Homeschool Curriculum course
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations Review
- Algebra II: Absolute Value Review
- Algebra II: Inequalities Review
- Algebra II: Working with Real Numbers
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Factoring Review
- Algebra II: Quadratic Equations Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Complex and Imaginary Numbers
- Algebra II: Rational Expressions Review
- Algebra II: Polynomials Review
- Algebra II: Polynomials Overview
- Algebra II: Graphing Polynomial Functions
- Algebra II: Conic Sections
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics Review
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistical Analysis
- Algebra II: Trigonometry Review
- Algebra II: Assignments & Projects
- Homeschool Resources for High School Algebra II