AP Precalculus Practice Test: Unit 3 Progress Check B (Sections 3.8 - 3.15)

My AP Precalculus Practice Tests are carefully designed to help students build confidence for in-class assessments, support their work on AP Classroom assignments, and thoroughly prepare them for the AP Precalculus exam in May.

### **3.8 The Tangent Function**:
- **Key Concept**: The tangent function relates the ratio of sine to cosine and is periodic with asymptotes where cosine equals zero.
- **Application**: Used to model slopes and angles, especially in situations involving angles of elevation and depression.

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### **3.9 Inverse Trigonometric Functions**:
- **Key Concept**: Inverse trigonometric functions (e.g., \( \sin^{-1}, \cos^{-1}, \tan^{-1} \)) give angles from known trigonometric values.
- **Application**: Useful for finding angles when given a trigonometric ratio.

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### **3.10 Trigonometric Equations and Inequalities**:
- **Key Concept**: Trigonometric equations and inequalities involve solving for angles that satisfy certain trigonometric conditions.
- **Application**: Used to solve problems in physics, engineering, and geometry involving angles and periodic functions.

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### **3.11 The Secant, Cosecant, and Cotangent Functions**:
- **Key Concept**: The secant, cosecant, and cotangent are the reciprocals of cosine, sine, and tangent, respectively.
- **Application**: These functions are important for solving trigonometric identities and equations.

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### **3.12 Equivalent Representations of Trigonometric Functions**:
- **Key Concept**: Trigonometric functions can be represented in different forms (e.g., using identities or reciprocal functions) for simplification.
- **Application**: These representations help solve complex trigonometric problems.

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### **3.13 Trigonometry and Polar Coordinates**:
- **Key Concept**: Polar coordinates represent points in the plane using a radius and angle instead of \(x\) and \(y\).
- **Application**: Trigonometry is used to convert between polar and Cartesian coordinates and analyze graphs in polar form.

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### **3.14 Polar Function Graphs**:
- **Key Concept**: Polar graphs plot functions in terms of radius and angle, often yielding unique shapes like circles or spirals.
- **Application**: Polar graphs are used in navigation, physics, and engineering, especially when circular or rotational symmetry is involved.

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### **3.15 Rates of Change in Polar Functions**:
- **Key Concept**: Rates of change in polar functions involve calculating how the radius changes with respect to the angle.
- **Application**: These calculations are crucial for analyzing motion along curved paths, such as orbits or gears.

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This condensed version highlights the main concepts and their uses in each section.

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

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