MATH& 142 Pre-Calculus II

5 credits

Precalculus II includes the study of the properties, graphs, and applications of the trigonometric functions and their inverses with an emphasis on identities and solving equations. This course also introduces vectors, polar coordinates and graphs, and parametric equations.

Prerequisites: MATH& 141.
Quarters Offered: Fall, Winter, Spring

Student Outcomes/Competencies:
Upon successful completion of this course students will be able to:

Measure angles in degrees and radians and relate them to arc length
Identify reference angles and coterminal angles
Solve applied problems involving arc length, linear/angular speed, and the area of a circular sector
Link the graphical, numeric, and symbolic definitions of the trigonometric functions in terms of the unit circle
Solve problems involving right triangles and unit circles using the definitions of the trigonometric functions
Apply the law of sines and law of cosines to solve for unknown sides and angles of triangles, and solve applied problems associated with these laws
Graph the trigonometric functions and their transformations
Identify key features including amplitude, period, and phase shifts from a graph, formula, table, or verbal description
Use trigonometric functions to model periodic behavior described numerically or verbally
Use the inverse trigonometric functions to solve equations
Prove trigonometric identities and use identities to algebraically solve trigonometric equations
Graph complex numbers and write complex numbers in trigonometric form
Perform operations with vectors and use them to solve problems (both graphically and component-wise)
Relate coordinates and equations in polar form to coordinates and equations in rectangular form
Graph polar equations
Relate equations and graphs in parametric form to equations and graphs in rectangular form
Write clear, correct, and complete solutions to mathematical problems utilizing proper mathematical notation and appropriate language
Use exact and approximate solutions when appropriate
Use problem solving skills, pattern recognition, substitution, structural rules, and quantitative modeling to solve problems involving trigonometric functions, vectors, systems of equations, alternative coordinate systems, and parametric equations