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Apr 19, 2024
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MATH& 142 Precalculus II (5 credits)
Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Prerequisite MATH& 141 with a grade of at least 2.0, suitable placement test score, or instructor permission.
Course Description
Families of trigonometric functions, their inverses, properties, graphs, and applications. Trigonometric equations and identities. Laws of sines and cosines. Polar coordinates and graphs. Parametric equations. Elementary vector operations.
Student Outcomes
A. Angles and Radian Measure
1. Convert radians to degrees and vice versa.
2. Solve applied problems involving arc length and linear/angular speed.
3. Determine or calculate the reference angle for a given angle and compute or determine angles coterminal with a given angle.
B. Trigonometric Functions and their Inverses
4. Apply the definitions of the trigonometric functions in terms of right triangles to solve for missing sides and angles of right triangles.
5. Apply the definitions of the trigonometric functions in terms of the unit circle to state the coordinates of a point on a circle in terms of sine and cosine.
6. Given a trigonometric function value for an angle, determine the other five trigonometric function values for the same angle without solving for the angle.
7. Solve applied problems involving right triangle trigonometry.
8. Recall or derive trigonometric function values for pi/6, pi/4, pi/3, pi/2, and pi as well as angles which are coterminal to these or have these as reference angles without outside reference or calculator.
9. Apply the law of sines and the law of cosines to solve for unknown sides and angles of triangles and solve applied problems associated with these laws.
10. Sketch the graphs of trigonometric functions, their transformations, and their inverses and state the domain and range of these functions.
11. Identify the amplitude, period, midline (vertical shift), and phase shift (or horizontal shift) from a graph, formula, table, or verbal description.
12. Determine a formula given the graph or table of a standard or transformed trigonometric function.
13. Use trigonometric functions to model periodic behavior (e.g., ferris wheels, daylight hours, tides, etc.).
14. Solve applied problems involving harmonic motion including problems with changing amplitude and/or midlines.
15. Evaluate inverse trigonometric functions involving the basic angles without the use of a calculator, considering the domain and range of these functions.
16. Convert trigonometric expressions such as cos(arctan x) into algebraic expressions.
C. Trigonometric Equations and Identities
17. Solve trigonometric equations for all solutions, providing exact or approximate solutions as appropriate.
18. Prove trigonometric identities that require multiple steps, other trigonometric identities, and algebraic manipulation.
19. Apply the addition and subtraction formulas, double angle formulas, and algebraic techniques to solve equations and simplify expressions.
D. Polar Coordinates and Graphs
20. Convert polar coordinates into rectangular coordinates and vice versa.
21. Convert polar equations into rectangular equations and vice versa.
22. Sketch the graphs of polar equations using a calculator, and sketch the graph of simple polar equations by hand.
E. Introduction to Vectors
23. Convert between direction and magnitude and component form of a vector
24. Perform basic operations with vectors (addition, subtraction, scalar multiplication) graphically and component-wise.
25. Solve vector application problems such as navigation and resultant forces, including problems where vectors are specified by magnitude and direction.
F. Parametric Equations
26. Convert a set of parametric equations into a Cartesian equation and determine a parametrization of a Cartesian equation including identifying the bounds.
27. Sketch the graphs of parametric equations by hand and by calculator.
G. General Outcomes
28.Write clear, correct, and complete solutions to mathematical problems utilizing proper mathematical notation and appropriate language.
29. Determine whether an exact or approximate solution is more appropriate for a given problem.
30. Participate actively and responsibly in all course activities.
31. Link graphical, numeric, and symbolic approaches when interpreting situations and analyzing problems.
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