Anne Arundel Community College

MAT 142: Trigonometry & Analytical Geometry



CATALOG DESCRIPTION:

A study of trigonometry and advanced algebra to prepare for calculus. Trigonometric topics include angle measurement, definitions of the six trigonometric functions from the right triangle and unit circle perspectives, graphs, identites, inverses, and equations. Algebraic topics include conic sections, polar coordinates, and a review of functions and graphs.

Prerequisite: MAT 131.

Note: Credit is not given for both MAT 142 and MAT 105 or MAT 142 and MAT 121 or MAT 142 and MAT 151.

LEARNING OBJECTIVES:

Upon completion of this course, the student will be able to:
  1. solve equations involving trigonometric, polynomial, rational, exponential, logarithmic, radical, and absolute value expressions.
  2. graph trigonometric, polynomial, piece-wise defined, rational, exponential, and logarithmic relations, and conic sections.
  3. analyze graphs of trigonometric, polynomial, piece-wise defined, rational, exponential, and logarithmic functions, and conic sections.
  4. perform algebraic operations on functions.
  5. model problems from the natural and social sciences with the appropriate algebraic or trigonometric equation or function.

COURSE OUTLINE:

Review of Functions and Graphs:
  • Functions
  • Graphs of Functions
  • Transformations of Functions
  • Combining Functions
  • One-to-One Functions and Their Inverses

Advanced Algebra Topics:
  • Compound Fractions
  • Solving Equations
  • Long and Synthetic Division
  • Exponential and Logarithmic Modeling
  • Absolute Value Expressions
  • Simplifying Complex Expressions

Trigonometric Functions & Applications:
  • Angle Measure
  • Trigonometry of Right Triangles
  • Trigonometric Functions of Angles
  • The Unit Circle
  • Trigonometric Functions of Real Numbers
  • The Law of Sines
  • The Law of Cosines
  • Trigonometric Graphs
  • More Trigonometric Graphs

Analytic Trigonometry:
  • Trigonometric Identities
  • Addition and Subtraction Formulas (Writing A sin x + B cos x as a single sine or cosine may be omitted.)
  • Double Angle, Half Angle Formulas (Sum-to-product formulas may be omitted.)
  • Inverse Trigonometric Functions
  • Trigonometric Equations

Conic Sections:
  • Parabolas
  • Ellipses and Circles
  • Hyperbolas

Polar Coordinates:
  • Polar Coordinate System
  • Graphs of Polar Equations

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