AP Precalculus Section 3.12 Example: Solving Trigonometric Equations Using Factoring (Example 4)

Random AP Precalculus Problems (I found on the Internet). These are not official AP Collegeboard examples, but they will definitely get the job done!

Solving a trigonometric equation by factoring involves the following steps:

1. **Identify the Equation:**
Start with the given trigonometric equation.

2. **Apply Trigonometric Identities:**
Use trigonometric identities to simplify the equation, such as Pythagorean, double-angle, or sum-to-product identities.

3. **Rearrange the Equation:**
Rearrange the equation to consolidate terms on one side, setting it equal to zero.

4. **Factor the Expression:**
Factor the expression by identifying common factors or using factoring techniques.

5. **Set Each Factor Equal to Zero:**
Use the zero-product property to set each factor equal to zero.

6. **Solve for \(x\):**
Solve the resulting equations for \(x\) to obtain potential solutions.

7. **Check for Extraneous Solutions:**
Verify each solution in the original equation to ensure validity.

8. **Write Down the Final Solution Set:**
Present the validated solutions as the final solution set.

Remember, the specific trigonometric identities and factoring techniques applied depend on the form of the original equation. Familiarity with these identities and algebraic methods is essential for successful application.

The Topics covered in AP Precalculus are...

1.1 Change in Tandem
1.2 Rates of Change
1.3 Rates of Change in Linear and Quadratic Functions
1.4 Polynomial Functions and Rates of Change
1.5 Polynomial Functions and Complex Zeros
1.6 Polynomial Functions and End Behavior
1.7 Rational Functions and End Behavior
1.8 Rational Functions and Zeros
1.9 Rational Functions and Vertical Asymptotes
1.10 Rational Functions and Holes
1.11 Equivalent Representations of Polynomial and Rational Expressions
1.12 Transformations of Functions
1.13 Function Model Selection and Assumption Articulation
1.14 Function Model Construction and Application
2.1 Change in Arithmetic and Geometric Sequences
2.2 Change in Linear and Exponential Functions
2.3 Exponential Functions
2.4 Exponential Function Manipulation
2.5 Exponential Function Context and Data Modeling
2.6 Competing Function Model Validation
2.7 Composition of Functions
2.8 Inverse Functions
2.9 Logarithmic Expressions
2.10 Inverses of Exponential Functions
2.11 Logarithmic Functions
2.12 Logarithmic Function Manipulation
2.13 Exponential and Logarithmic Equations and Inequalities
2.14 Logarithmic Function Context and Data Modeling
2.15 Semi-log Plots
3.1 Periodic Phenomena
3.2 Sine, Cosine, and Tangent
3.3 Sine and Cosine Function Values
3.4 Sine and Cosine Function Graphs
3.5 Sinusoidal Functions
3.6 Sinusoidal Function Transformations
3.7 Sinusoidal Function Context and Data Modeling
3.8 The Tangent Function
3.9 Inverse Trigonometric Functions
3.10 Trigonometric Equations and Inequalities
3.11 The Secant, Cosecant, and Cotangent Functions
3.12 Equivalent Representations of Trigonometric Functions
3.13 Trigonometry and Polar Coordinates
3.14 Polar Function Graphs
3.15 Rates of Change in Polar Functions

I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:

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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

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