About This Chapter
Explorations in Core Math Algebra 2 Chapter 11: Trigonometric Graphs and Identities - Chapter Summary and Learning Objectives
This chapter will help you analyze trigonometric graphs and identities. Lessons will explain how to graph a number of trigonometric functions and guide you to an understanding of various identities. You can focus on increasing what you know about:
- Graphs of the sine, cosine and tangent
- How to graph the cosecant, secant and cotangent
- Trigonometric, double-angle and half-angle identities
- Sum and difference identities
- Unit circles
- Trigonometric equations
|Graphing Sine and Cosine||Evaluate how sine and cosine can be graphed on a unit circle.|
|Graphing Sine and Cosine Transformations||Calculate what happens to sine and cosine waves when they're transformed.|
|Graphing the Tangent Function: Amplitude, Period, Phase Shift & Vertical Shift||Assess how tangent functions can be graphed and transformed.|
|Graphing the Cosecant, Secant & Cotangent Functions||Develop the ability to identify graphs of the cosecant, secant and cotangent with and without transformations.|
|Trigonometric Identities: Definition & Uses||Consider and recognize different identities.|
|Verifying Trigonometric Identities with Unit Circles||Focus on using the unit circle to validate trigonometric identities.|
|Applying the Sum & Difference Identities||Compare the six sum and difference identities.|
|Double-Angle Identities: Uses & Applications||Negotiate the usage of double-angle identities in trigonometry.|
|Half-Angle Identities: Uses & Applications||Explain how to use half-angle identities to simplify trigonometry problems.|
|Writing & Revising Trigonometric Equations||Develop your ability to write and revise trigonometric equations.|
1. Graphing Sine and Cosine
In trigonometry, sine and cosine are functions used to study right angles. Learn about graphing sine and cosine, and explore how to do the wave. Review the unit circle, sine wave, cosine wave, period, and amplitude, and understand how these help create the sine and cosine graph.
2. 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.
3. 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.
4. Graphing the Cosecant, Secant & Cotangent Functions
The cosecant acts as the reciprocal of the sine, the secant is the reciprocal of the cosine, and the cotangent is the reciprocal of the tangent function. Learn how these appear on graphs, and examine the shifting methods using transformations.
5. Trigonometric Identities: Definition & Uses
Trigonometric identities are equations that are always true for trigonometric functions. Learn about the definition and kinds of trigonometric identities and explore the uses of trigonometric identities through examples.
6. 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.
7. Applying the Sum & Difference Identities
Discover how to apply the sum and difference identities in trigonometry which are used to find sine, cosine, and the tangent of two given angles. Review the sum and difference identities before taking a closer look at two examples.
8. Double-Angle Identities: Uses & Applications
Double-angle identities are similar to half-angle identities, as they are true statements about double-angles. Learn to use and apply these identities to two example problems.
9. Half-Angle Identities: Uses & Applications
Half-angle identities are simply true statements about half-angles that can simplify certain trigonometry problems. Learn the ways these identities are used and applied through two example scenarios provided.
10. Writing & Revising Trigonometric Equations
Read this lesson to learn how you can write a trigonometric equation for the Ferris wheel problem and then rewrite it to find the height of a rider as the Ferris wheel spins around.
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Other chapters within the Explorations in Core Math - Algebra 2: Online Textbook Help course
- Explorations in Core Math Algebra 2 Chapter 1: Foundations for Functions
- Explorations in Core Math Algebra 2 Chapter 2: Quadratic Functions
- Explorations in Core Math Algebra 2 Chapter 3: Polynomial Functions
- Explorations in Core Math Algebra 2 Chapter 4: Exponential and Logarithmic Functions
- Explorations in Core Math Algebra 2 Chapter 5: Rational and Radical Functions
- Explorations in Core Math Algebra 2 Chapter 6: Properties and Attributes of Functions
- Explorations in Core Math Algebra 2 Chapter 7: Probability
- Explorations in Core Math Algebra 2 Chapter 8: Data Analysis and Statistics
- Explorations in Core Math Algebra 2 Chapter 9: Sequences and Series
- Explorations in Core Math Algebra 2 Chapter 10: Trigonometric Functions
- Explorations in Core Math Algebra 2 Chapter 12: Conic Sections