
20222023 College Catalog [ARCHIVED CATALOG]

MAT 189  Precalculus II [SUN# MAT 1187] 3 Credits, 3 Contact Hours 3 lecture periods 0 lab periods
Continuation of MAT 188 . Collegelevel trigonometry. Includes trigonometric functions, angle measure, graphs, identities, equations, polar coordinates, conic sections, and calculator use. May also include parametric equations, vectors, and complex numbers.
Prerequisite(s): Within the last three years: MAT 188 with a grade of C or better, or required score on the mathematics assessment test. Recommendation: This course is intended as an intensive preparation for students who plan to continue with Calculus. Information: No more than 7 credits may be applied toward graduation from the following list of courses: MAT 151 , MAT 188 , and MAT 189. A graphing calculator is required for this course and will be used extensively. GenEd: Meets AGEC  MATH; Meets CTE  M&S.
Course Learning Outcomes
 Solve trigonometric equations and verify trigonometric identities.
 Graph trigonometric functions polar equations, and conic sections.
 Solve triangles and real world applications.
Performance Objectives:
 Convert between radians and degrees measures.
 Define, graph, and evaluate the six trigonometric functions and their inverses.
 Solve trigonometric equations algebraically and graphically.
 Use trigonometric identities to simplify expressions and solve equations.
 Graph polar equations; convert between rectangular and polar coordinates.
 Use the standard equations for conic sections and sketch their graphs; identify types of conic sections and determine their features.
 Use a graphing calculator to evaluate, graph, and analyze functions.
 Solve application problems.
Outline:
 Trigonometric Functions
 Angle measure
 Definition and graphs of the six trigonometric functions
 Trigonometric Identities
 Basic, Pythagorean and Reciprocal
 Sum and difference formulas
 Double angle and half angle formulas
 Sum to product and product to sum (optional)
 Verification of identities
 Inverse trigonometric functions
 Law of Sines and Law of Cosines
 Trigonometric Equations
 Applications
 Polar Coordinates
 Conversion between rectangular and polar coordinates
 Graphs of polar equations
 Conic Sections
 Standard equations: Parabolas, Circles, Ellipses
 Identification of type of conic section
 Determination of features: center, vertices
 Optional:
 Hyperbolas
 Determination of foci, asymptotes
 Calculator Use
 Numerical calculations and evaluation of functions
 Graphs and analysis of functions
 Additional Topics: select at least one
 Complex Numbers
 Definition and graphical representation
 Operations
 Conversion between standard form and polar form
 DeMoivre’s Theorem
 Vectors
 Addition, scalar multiplication
 Magnitude
 Conversion from rectangular to polar form
 Applications
 Parametric Equations

