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Section 7.4 Basic Trigonometric Equations

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1 Section 7.4 Basic Trigonometric Equations
Chapter 7 – Analytic Trigonometry Section 7.4 Basic Trigonometric Equations 7.4 - Basic Trigonometric Equations

2 7.4 - Basic Trigonometric Equations
Definitions Trigonometric Equation An equation that contains trigonometric functions is called a trigonometric equation. Basic Trigonometric Equation Solving any trigonometric equation always reduces to solving a basic trigonometric equation – an equation in the form T() = c where T is a trigonometric function and c is a constant. 7.4 - Basic Trigonometric Equations

3 Solving Basic Trig Equations
The next few examples will show how we can solve basic trigonometric equations. 7.4 - Basic Trigonometric Equations

4 Example – pg. 522 # 5 Solve the given equation.
This means we want to find the solutions to the problem above for the following: the primary cycle. all solutions. Check by graphing.

5 Example – pg. 523 #17 Solve the given equation, and list six specific solutions.

6 Example – pg. 523 # 21 Solve the given equation, and list six specific solutions.

7 7.4 - Basic Trigonometric Equations
Example – pg. 523 # 23 Solve the given equation, and list six specific solutions. 7.4 - Basic Trigonometric Equations

8 Solving Trigonometric Equations
In the next example, we will solve a trigonometric equation that is algebraically equivalent to a basic trigonometric equation. 7.4 - Basic Trigonometric Equations

9 7.4 - Basic Trigonometric Equations
Examples – pg. 523 Find all solutions of the given equation. 7.4 - Basic Trigonometric Equations

10 Solving Trig Equations by Factoring
Factoring is one of the most useful techniques for solving equations, including trigonometric equations. The idea is to move all terms to one side of the equation, factor, and then use the Zero-Product Property. The next few examples will cover solving trigonometric equations by factoring. 7.4 - Basic Trigonometric Equations

11 7.4 - Basic Trigonometric Equations
Examples – pg. 523 Solve the given equation. 7.4 - Basic Trigonometric Equations

12 7.4 - Basic Trigonometric Equations
Try these problems… Solve the given equation. 7.4 - Basic Trigonometric Equations

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