AP Precalculus Review on Sections 3.8, 3.9, 3.10, 3.11, 3.12 (Reteaching and Test Practice Problems)

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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

In this video, I thoroughly describe and reteach the main components of the sections listed above found in the official College Board AP Precalculus course description found at https://apcentral.collegeboard.org/me.... Afterwords, I provide multiple examples and give descriptive solutions to AP Precalculus-style problems. Topics in this video include…

Sure, here's a brief description of each AP precalculus topic:

3.8 The Tangent Function:
The tangent function is a trigonometric function that represents the ratio of the length of the side opposite to an acute angle in a right triangle to the length of the adjacent side. It is commonly denoted as tan(θ) and is used extensively in trigonometry to solve problems involving angles and sides of triangles.

3.9 Inverse Trigonometric Functions:
Inverse trigonometric functions are functions that undo the action of trigonometric functions. They allow us to find the measure of an angle given the ratio of sides in a right triangle. Common inverse trigonometric functions include arcsin(x), arccos(x), and arctan(x), which represent the inverse of sine, cosine, and tangent functions, respectively.

3.10 Trigonometric Equations and Inequalities:
Trigonometric equations and inequalities involve expressions containing trigonometric functions. These equations and inequalities may involve solving for angles or finding possible solutions within given ranges. Techniques such as factoring, substitution, and trigonometric identities are often used to solve these types of equations and inequalities.

3.11 The Secant, Cosecant, and Cotangent Functions:
The secant, cosecant, and cotangent functions are reciprocal trigonometric functions. The secant function is the reciprocal of the cosine function, the cosecant function is the reciprocal of the sine function, and the cotangent function is the reciprocal of the tangent function. These functions have applications in trigonometry, calculus, and physics.

3.12 Equivalent Representations of Trigonometric Functions:
Trigonometric functions can be represented in different forms, including as ratios of sides in a right triangle, as points on the unit circle, and as periodic functions with specific properties. Equivalent representations allow for different perspectives and methods of analysis in solving trigonometric problems and understanding trigonometric functions.

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