About This Chapter
Using Trigonometric Functions - Chapter Summary
Just because you don't know all the measurements of a shape doesn't mean you don't have the tools needed to find those measurements. These lessons will show you how to apply trigonometric functions to find unknown variables. Each lesson provides a thorough explanation of related mathematical laws, theorems, and formulas, complete with relevant examples. Most of the lessons include sample problems that walk you through all the necessary steps. At the end of each lesson, try answering the quizzes to verify if you have absorbed all the information. This chapter has been constructed to give you the skills needed to do the following:
- Point out the uses for cosine and sine
- Offer examples of cosecant, secant, and cotangent functions
- Review the first quadrant of the unit circle
- Show how to connect right triangles to cosine and sine with unit circles
- Determine circular trigonometric functions
- Differentiate the properties and types of special right triangles
- Establish how special angles have trigonometric function values
- Outline the applications for the law of sines and the law of cosines
- Evaluate the double angle formula
- Figure out how to convert radians into degrees
1. 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.
2. Other Trigonometric Functions: Cotangent, Secant & Cosecant
After watching this video lesson, you will understand how the trigonometric functions cotangent, secant, and cosecant are related to the sine, cosine, and tangent functions.
3. 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.
4. 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.
5. Practice Problems with Circular Trigonometric Functions
After watching this video lesson, you will be able to use the unit circle to help you find your answer to trig problems without making too many calculations. Watch and learn how you can find your angle in radians on the unit circle.
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. Trigonometric Function Values of Special Angles
After watching this video lesson, you will better understand the six trigonometric functions. You will also know what special angles there are and what the trigonometric values for these special angles are.
8. 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.
9. 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.
10. 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.
11. 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.
12. Converting 225 Degrees to Radians: How-To & Steps
How do you change from an angle measured in degrees to an angle measured in radians? Find out what a radian is and how to convert between the two units by reading this step by step lesson.
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Other chapters within the Precalculus: High School course
- Working With Inequalities Review
- Absolute Value Equations Review
- Working with Complex Numbers Review
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Graphing Piecewise Functions
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions Review
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Analytic Geometry & Conic Sections Review
- Polar Coordinates and Parameterizations