MATH& 142 - Precalculus II

Credits: 5
Variable Credit Course: No

Lecture Hours: 55
Lab Hours: 0
Worksite/Clinical Hours: 0
Other Hours (LIA/Internships): 0

Course Description: The second course in a two-course sequence for students who intend to take calculus beginning with Math& 151. Topics include right triangle trigonometry and applications, solutions of oblique triangles, unit circle trigonometry and applications, identities, inverse trigonometric functions, solving equations, graphing and modeling, introduction to polar coordinates, complex numbers, vectors and conic sections. Graphing technology required.

Prerequisite: MATH& 141 with a grade of C or higher, or equivalent math placement score.
Distribution Requirements:

Natural Sciences Distribution Requirement
Quantitative

Meets FQE Requirement: No
Integrative Experience Requirement: No

Student Learning Outcomes

Analyze the relationships between right triangles, circles, and trigonometric functions using radian or degree measurements.
Use trigonometric functions and their inverses to find angles or lengths involving right triangles.
Solve geometric problems using trigonometric relationships including right triangle identities, the Law of Sines, and the Law of Cosines.
Graph and analyze the graphs of trigonometric functions using transformations.
Verify trigonometric identities and use them to solve equations.
Use algebraic and geometric vectors to solve elementary vector problems involving trigonometry.
Identify and graph polar functions and convert between polar and rectangular form.
Analyze and graph conic sections.
Use technology to analyze trigonometric functions and equations.

Course Contents

Trigonometric Functions. Radian and degree measures. The unit circle. Right triangle trigonometry and applications. Solving oblique triangles using the Law of Sines and Law of Cosines. Graphs of trigonometric functions. Inverse trigonometric functions and their graphs. Applications and modeling including harmonic motion.
Analytic Trigonometry. Fundamental trigonometric identities. Verifying trigonometric identities. Sum and Difference formulas. Double angle, half angle, and product to sum (optional) formulas. Solving trigonometric equations.
Applied Trigonometry. Polar coordinates. Graphs of polar equations. Converting between polar and rectangular forms. Polar form of complex numbers (optional). Multiplication and addition of complex numbers in polar form (optional). DeMoivre’s formulas for powers and roots of complex numbers (optional). Vectors in two dimensions. Applications using vectors. The dot product and applications. The cross product (optional).
Other Topics. Conic sections. Polar form of conics (optional). Rotation of axes (optional). Plane curves and parametric equations (optional).

Instructional Units: 5