About This Chapter
Introduction to Trigonometry - Chapter Summary and Learning Objectives
Also known as 'trig,' this branch of math grew from geometry and is used in astronomy, navigation and surveying. In this chapter, you can extend your geometric knowledge and make further use of the Pythagorean Theorem to find distances and solve right triangles. You can also learn the laws of sines and cosines in addition to practicing their applications. This chapter is designed to teach you:
- Strategies for visualizing geometry problems
- Calculations for the volumes of basic shapes
- Use of the Pythagorean Theorem for finding distance
- Sines, cosines and tangents
- Similarity and trigonometric ratios
- How to solve right triangles
- How to find area
- Applications for the Laws of Sines and Cosines
|How to Solve Visualizing Geometry Problems||Apply a graphical and hands-on approach to visualizing geometry problems.|
|How to Calculate the Volumes of Basic Shapes||Calculate the volume of spheres, pyramids and other basic shapes.|
|Finding Distance with the Pythagorean Theorem||Apply the Pythagorean Theorem to find distance between points.|
|Trigonometry: Sine and Cosine||Graph sines and cosines; describe them on right triangles.|
|Trigonometry and the Pythagorean Theorem||Use trigonometry in conjunction with the Pythagorean Theorem.|
|Introduction to Sines, Cosines and Tangents||Learn about the basic trigonometric ratios.|
|Trigonometric Ratios and Similarity||Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.|
|Practice Finding the Trigonometric Ratios||Apply what you've learned to find trigonometric ratios in practice problems.|
|Sine and Cosine of Complementary Angles||Explain and use the relationship between the sine and cosine of complementary angles.|
|The Pythagorean Theorem: Practice and Application||Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.|
|Solving Right Triangles||Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.|
|Problems Requiring Solving Right Triangles||Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.|
|Using A = ½ ab sin (C) to Find Area||Derive the formula A = ½ ab sin (C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.|
|The Law of the Sines||Prove the Laws of Sines and Cosines and use them to solve problems.|
|The Law of the Cosines||Prove the Laws of Sines and Cosines and use them to solve problems.|
|Practice Applying the Law of the Sines and the Law of the Cosines||Understand and apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).|
1. How to Solve Visualizing Geometry Problems
A picture is worth a thousand words, but sometimes drawing that picture can be like doing origami with your eyes closed. Practice translating complex problems into simple, meaningful images in this lesson.
2. How to Calculate the Volumes of Basic Shapes
Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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: High School course
- High School Geometry: Foundations of Geometry
- High School Geometry: Logic in Mathematics
- High School Geometry: Introduction to Geometric Figures
- High School Geometry: Properties of Triangles
- High School Geometry: Triangles, Theorems and Proofs
- High School Geometry: Parallel Lines and Polygons
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Conic Sections
- High School Geometry: Geometric Solids
- High School Geometry: Analytical Geometry
- High School Geometry: Probability
- Teacher Resources for High School Geometry