About This Chapter
Introduction to Trigonometry - Chapter Summary
This chapter offers you an introductory view of trigonometry, including some of the fundamental theorems and concepts you must understand to solve trigonometric problems. Many of the lessons in this chapter use videos, which include the keywords, definitions, and formulas displayed on the screen. Entertaining animations and other visual aids further enrich our learning resources. At the end of the chapter, you will have developed the knowledge to:
- Use the Pythagorean theorem to determine distance
- Compare the uses of cosine and sine in trigonometry
- Explain each of the basic trig identities
- Point out the connection between the Pythagorean theorem and trigonometry
- Summarize the concepts of trigonometric similarity and ratios
- Determine trigonometric ratios
- Find the cosine and sine of complementary angles
- Use sine to determine the area of a triangle
- Establish the applications of the law of sines and the law of cosines
1. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
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. 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.
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. Trigonometric Ratios and Similarity
Where do terms like sine, cosine and tangent come from? In this lesson, we'll learn about how similarity with right triangles leads to trigonometric ratios.
6. Practice Finding the Trigonometric Ratios
So you know what sine, cosine and tangent are. Great! But how do you use them? Find out how in this lesson as we find missing sides and angles using trigonometric ratios.
7. Sine & Cosine of Complementary Angles
In this lesson, we'll look at the relationship between the sine and cosine of complementary angles. We'll discuss where this relationship comes from and explore examples of how it can be used.
8. Using Sine to Find the Area of a Triangle
Since you first started working with triangles in math class, chances are you've been exposed to the formula for the area of a triangle. However, that is only good if you know the height of the triangle. This lesson shows you how to get around that.
9. 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.
10. 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.
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Other chapters within the Geometry 101: Intro to Geometry course
- Basics of Geometry
- Logic & Proof in Mathematics
- Intro to Geometric Figures
- Triangle Properties & Construction
- Parallel Lines & Polygons
- Triangle Congruence
- Ratios & Proportions in Geometry
- Similar Polygons
- Quadrilaterals Overview
- Circles Overview
- Overview of Conic Sections
- 3D Geometry
- Analytical Geometry
- Non-Euclidean Geometry
- Studying for Geometry 101