MATH& 142 Precalculus II (5 credits)
Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Formerly MATH 122
Prerequisite MATH& 141 or equivalent with a grade of 2.0 or better
Course Description
This is the second of two courses in the precalculus sequence, which is designed to prepare students for calculus. Topics include trigonometric functions and their inverses, with an emphasis on using their properties to choose problem-solving strategies in context, including measurement and modeling. Concludes with an introduction to vectors, polar coordinates, and parametric equations.
Course Content
A. Angles and Radian Measure
Conversion between degrees and radians
Reference angles and coterminal angles
B. Trigonometric Functions
Special coordinates on a unit circle
Using one trigonometric function value to find other trigonometric function values
Graphs of trigonometric functions
Transformations of amplitude, period, midline (vertical shift), and phase shift (horizontal shift)
C. Inverse Trigonometric Functions
Domain and range of inverse trigonometric functions
Using inverse trigonometric functions to find angles
D. Trigonometric Equations and Identities
Solving trigonometric equations
Proving trigonometric identities
Using identities to solve equations and simplify expressions.
E. Polar Coordinates and Graphs
Converting between polar and rectangular coordinates
Converting between polar and rectangular equations
Graphing polar equations
F. Introduction to Vectors
Converting between direction and magnitude and component form of vectors
Geometric and component-wise operations with vectors
G. Parametric Equations
Converting between parametric and Cartesian equations
Sketching graphs of parametric equations
H. Applications
Applied problems involving arc length and linear/angular speed
Modeling periodic behavior
Modeling changing amplitude and/or midlines
Solving right triangles
Law of Sines and Law of Cosines
Vector application problems (navigation, resultant forces)
Parametric representation of motion
Student Outcomes
- Transition between various representations of trigonometric functions, such as coordinates on a unit circle, ratios between the sides of a right triangle, a function which accepts an angle as an input and gives a ratio as an output, and the periodic graph representing the function.
- Find values of the six trigonometric functions at common unit circle angles without the use of a calculator, using radians and degrees, and at other angles with the use of a calculator or by using appropriate identities.
- Analyze the effect of function transformations on the behavior of trigonometric functions and their properties, using algebraic, numerical, verbal, and graphical representations.
- Solve trigonometric equations within a specified interval using the relationship between appropriate domain restrictions of trigonometric functions and the ranges of their respective inverse functions, without a calculator for common values, and with a calculator for others.
- Use context to develop viable trigonometry-related problem-solving strategies, including the choice of appropriate representations of trigonometric functions and their inverses.
- Implement appropriate algebraic techniques to manipulate trigonometric expressions to achieve a desired goal, for example to prove a trigonometric identity or solve a trigonometric equation.
- Communicate solution processes including strategy choices in the context of trigonometry applied problems.
- Evaluate the reasonableness of a problem solution in the context of its mathematical and/or real-world assumptions.
Degree Outcomes
Quantitative & Symbolic Reasoning: Graduates utilize mathematical, symbolic, logical, graphical, geometric, or statistical analysis for the interpretation and solution of problems in the natural world and human society.
Critical, Creative and Reflective Thinking: Graduates will evaluate, analyze, synthesize, and generate ideas; construct informed, meaningful, and justifiable conclusions; and process feelings, beliefs, biases, strengths, and weaknesses as they relate to their thinking, decisions, and creations.
Effective Communication: Graduates will be able to craft and exchange ideas and information in a variety of situations, in response to audience, context, purpose, and motivation.
Lecture Contact Hours 50
Lab Contact Hours 0
Clinical Contact Hours 0
Total Contact Hours 50
Potential Methods
Discussions
Written Assignments
Projects
Case Studies
Presentations
Homework
Quizzes
Objective Tests
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