Learning Resources
Lesson
In this Focus you will revisit solving trigonometric equations. This concept was previously encountered in Mathematical Modeling, Book 2.
Before actually solving trigonometric equations, there are a few points to remember.
- Often, there are multiple solutions to an equation.
- It is important to use trigonometric identities to simplify an equation, where possible, and to identify any restrictions on the variable.
- It is often helpful to make the equation equal to zero and attempt to factor the given expression.
- Do not divide both sides of the equation by a common factor. You will lose roots.
Keeping the above suggestions in mind, solve each equation below, finding all possible values of x.
- 2cosx + 1 = 0
- 2sinx = cscx
- sin2x = sinx
- tanx cscx = 1
Once the questions are completed, you may check your solutions.
You should now be ready to begin Focus F as outlined on pages 254 to 256 of your text. Pay close attention to each of the examples. Hints and suggestions are provided for the examples, should you require assistance.
Some additional examples are provided below.
You should now attempt to answer the Focus Questions.
Activity
Focus Questions pages 256 & 257 #'s 24 - 27
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
Test Yourself
Solve each trigonometric equation below where x ? [0, 2
).
Solutions
1. 
2. 
3. 
4. 