About This Chapter
Solving Trigonometric Equations - Chapter Summary and Learning Objectives
The processes involved in solving trigonometric equations are a lot like the steps required to work with other types of functions. In fact, once you discover the relationship between trig functions and their inverses, you're off to the races. Use the lessons in this chapter to explore some of the basic properties of inverse trigonometric functions and take a look at their graphs, so you can successfully find or solve the following:
- Trigonometric equations with restricted domains
- Trigonometric equations with infinite solutions
- Sinusoidal functions for data sets
|How to Solve Trigonometric Equations for X||Examine the inverse operations of trigonometric functions, trigonometric restrictions and the steps involved in solving equations for x.|
|Solving Trigonometric Equations with Identities and Inverse Functions||Learn how basic trigonometric identities and inverse trigonometric functions can be used to solve trigonometric equations.|
|Properties of Inverse Trigonometric Functions||Explore properties of inverse functions for sine, cosine and tangent. Learn to recognize their graphs.|
|Solving Trigonometric Equations with Restricted Domains||Use algebra or a graphing utility to find the values of inverse trigonometric functions and solve trigonometric equations with restricted domains.|
|Solving Trigonometric Equations with Infinite Solutions||Solve trigonometric equations with infinite solutions, either by using algebra or a graphing utility.|
|Finding the Sinusoidal Function||Model a given data set with the appropriate sinusoidal function. Relate the model's parameters to the situation or data set.|
1. Solve Trigonometric Equations with Identities & Inverses
After watching this video lesson, you will be able to solve trigonometric equations by making use of trigonometric identities and inverses. Learn the steps to take to get to your solution.
2. 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.
3. Properties of Inverse Trigonometric Functions
After watching this video lesson, you will understand why our inverse trigonometric functions have a limited range. Learn what this does. Also learn the notation for these functions.
4. Solving Trigonometric Equations with Restricted Domains
After watching this video lesson, you will be able to find the right answer for a trigonometric equation with a restricted domain. Learn what it means to have a restricted domain and what you need to do to find your answer.
5. Solving Trigonometric Equations with Infinite Solutions
Watch this video lesson and you will learn that all trigonometric equations have an infinite set of solutions. But you will also see that we can still go ahead and solve our equations and find concrete answers.
6. Finding the Sinusoidal Function
After watching this video lesson, you will be able to write a sinusoidal function to represent any wave that you see. Learn what parts of the function make the wave shift up, down, to the left, and to the right.
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Other chapters within the High School Precalculus Textbook course
- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Functions: Basics for Precalculus
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Polynomial Functions Basics
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Sets in Algebra