MTH 112Z Precalculus 2: Trigonometry

Lecture Hours: 4
Credits: 4

A course primarily designed for students preparing for calculus and related disciplines. This course explores trigonometric functions and their applications as well as the language and measurement of angles, triangles, circles, and vectors. These topics will be explored symbolically, numerically, and graphically in real-life applications and interpreted in context. This course emphasizes skill building, problem solving, modeling, reasoning, communication, connections with other disciplines, and the appropriate use of present-day technology.

Prerequisite: Placement into WR 115 (or higher), or completion of WR 090 (or higher); and placement into MTH 112Z (or higher), or completion of MTH 111Z (or higher) or equivalent course as determined by instructor; or consent of instructor. (All prerequisite courses must be completed with a grade of C or better.)
Student Learning Outcomes:
Common Course Number Outcomes:

Translate among various systems of measure for angles including radians, degrees, and revolutions.
Represent, manipulate, and evaluate trigonometric expressions in terms of sides of a right triangle and in terms of the coordinates of a unit circle.
Graph, transform, and analyze trigonometric functions using amplitude, shifts, symmetry, and periodicity.
Manipulate trigonometric expressions and prove trigonometric identities.
Solve trigonometric equations using inverses, periodicity, and identities.
Define, represent, and operate with vectors both geometrically and algebraically.
Apply the law of sines and the law of cosines to determine lengths and angles.
Use variables, trigonometric functions, and vectors to represent quantities, create models, find solutions, and communicate an interpretation of the results.
Determine the reasonableness and implications of mathematical methods, solutions, and approximations in context.

AAOT Outcomes:

Use appropriate mathematics to solve problems.
Recognize which mathematical concepts are applicable to a scenario, apply appropriate mathematics and technology in its analysis, and then accurately interpret, validate and communicate the results.

Content Outline

Trigonometric Functions
- Special angles and their exact trigonometric values
- Graphs of trigonometric functions
- Amplitude, period, translations of trigonometric functions
- Inverses of trigonometric functions
Trigonometric Equations
- Solving equations graphically, numerically, and symbolically
- Proving identities
Numerical Trigonometry
- Right triangle applications
- The Laws of Sine and Cosine
Vectors and parametric equations.
- Representations of vectors in rectangular and polar forms
- Applications to physical problems
- Dot product and applications to physical and geometric problems
- Parametric representations
- Graphing parametric equations