About This Chapter
Trigonometry - Chapter Summary and Learning Objectives
This chapter focuses on some basic concepts of trigonometry. These beginner level lessons will introduce you to concepts like graphing the sine, cosine and tangent functions. You'll get to learn about the unit circle and shifts in graphs. We have lessons that will also cover right triangles and the relationship of right triangles to sine and cosine. Special right triangle properties will also be covered. Some of the specific concepts you'll learn in this chapter include:
- How the Law of Sines relates to right triangles
- The relationship between the Law of Cosine and the Pythagorean Theorem
- How to use the Double Angle Formula
- How to convert between radians and degrees
- How to solve trigonometric equations for x
- Basic trigonometry identities
|Graphing Sin/Cos & Transformations||Learn to graph sine and cosine unit circle and explain shifts.|
|Graphing the Tangent Function: Amplitude, Period, Phase Shift & Vertical Shift||Discover how to graph the tangent function and learn the concepts of amplitude, period, phase shift and vertical shift.|
|Unit Circle: Memorizing the First Quadrant||Study the first quadrant of the unit circle.|
|Right Triangles||Examine right triangles as they relate to sine and cosine.|
|Special Right Triangles (3-6-9, 45)||Explore the common properties of special right triangles.|
|Law of Sines||Find out how to use two angles and a side to define the entire triangle.|
|Law of Cosines||Use the Law of Cosine and relate it to the Pythagorean Theorem.|
|Double Angle Formula||Take a look at how to use the angle sum formula.|
|Converting Between Radians and Degrees||Learn how to convert angles in radians to degrees and degrees to radians.|
|How to Solve Trigonometric Equations for x||Practice solving trigonometric equations for x.|
|List of the Basic Trig Identities||Explore the basic trigonometry identities.|
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. Special Right Triangles: Types and Properties
Not all right triangles are the same. In this lesson, we'll look at two special right triangles (30-60-90 and 45-45-90) that have unique properties to help you quickly and easily solve certain triangle problems.
7. 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.
8. 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.
9. The Double Angle Formula
When you encounter a doubled angle, there are special formulas that can help you handle trigonometric value. In this lesson, we'll define and practice using the double angle formulas for sine, cosine and tangent.
10. 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.
11. 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.
12. List of the Basic Trig Identities
There are specific trig functions that have very special and very simple relationships with each other. Learn the main one and how you can use it to understand the others.
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Other chapters within the Math 103: Precalculus course
- Evaluating Exponential and Logarithmic Functions
- Foundations of Linear Equations
- Graphing and Rational Equations
- Factoring and Graphing Quadratic Equations
- Exponents and Polynomials
- Piecewise and Composite Functions
- Geometry and Trigonometry
- How to Use a Scientific Calculator
- Studying for Math 103