Course Outline for Mathematics 22
Trigonometry with Analytic Geometry

Effective: Fall 2023
SLO Rev: 11/12/2021
Catalog Description:
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. identify special triangles and their related angle and side measures;
  2. evaluate the trigonometric function of an angle in degree and radian measure;
  3. manipulate and simplify a trigonometric expression;
  4. solve trigonometric equations, triangles, and applications;
  5. graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs;
  6. evaluate and graph inverse trigonometric functions;
  7. prove trigonometric identities;
  8. convert between polar and rectangular coordinates and equations;
  9. graph polar equations;
  10. represent a vector (a quantity with magnitude and direction) in the form and ai+bj;
  11. represent lines and planes using vectors;
  12. represent geometric curves using functions and parametric equations;
  13. represent operations on complex numbers geometrically.
Course Content:
  1. Analytic Geometry
    1. Parallel and perpendicular lines
    2. Distance formula
    3. Midpoint formula
    4. Conic Sections
      1. Circles
      2. Ellipses
      3. Hyperbolas
    5. Equation and graph of a circle
    6. Equation and graph of ellipse as a transformation from those of a circle
    7. Parametric equations for curves
  2. Geometry
    1. Area formulas for plane figures
    2. Volume formulas for solids
    3. Surface area for solids
    4. Congruent and similar figures
  3. Rectangular coordinates, angles, and radian measure
  4. Definitions of the six trigonometric functions according to:
    1. The right triangle
    2. The unit circle
    3. The rectangular coordinate system
  5. Graphs of trigonometric functions
    1. Period
    2. Amplitude
    3. Phase shift
    4. Asymptotes
  6. Inverse trigonometric functions and their graphs
    1. Domain and range
    2. Asymptotes
  7. Solving triangles
    1. Special triangles
    2. Law of Sines
    3. Law of Cosines
    4. Applications
  8. Trigonometric formulas
  9. Proving trigonometric identities
  10. Trigonometric equations and inequalities
    1. Algebraic techniques
    2. Graphical techniques
  11. Trigonometric models and applications, including the use of parametric equations
  12. Introduction to vectors in two and three dimensions
    1. Properties of vector space
    2. Inner and cross product
    3. Parametric description of lines and planes using vectors
    4. Geometry of complex numbers 
    5. DeMoivre's Theorem
  13. Polar coordinate system
    1. Points in the polar plane
    2. Polar equations
    3. Graphing
Methods of Instruction:
  1. Lecture/Discussion
  2. Distance Education
  3. Class and group discussions
  4. Hands-on Activities
Assignments and Methods of Evaluating Student Progress:
  1. Ten minutes after a furnace is turned on the temperature in a room reaches 74F and the furnace turns off. It takes two minutes for the room to cool to 70F and two minutes for the furnace to bring the temperature back up to 74F. Assuming that the temperature after the first 10 minutes can be modeled by a sine function, construct a function f(t) modeling the temperature in the room t minutes after the room first reaches 74F.
  2. Solve for T in [0, 2pi): cos(2T)=cos T
  3. Solve the oblique triangle with sides a=9, b=6, and c=4.
  1. Exams/Tests
  2. Final Examination
  3. Quizzes
Upon the completion of this course, the student should be able to:
  1. critically analyze mathematical problems using a logical methodology;
  2. communicate mathematical ideas, understand definitions, and interpret concepts;
  3. increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. Jay Abramson (2021). Algebra and Trigonometry (2e/e). OpenStax https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
  1. Dugopolski, D. (2020). Trigonometry (5th). Pearson.
Abbreviated Class Schedule Description:
Students completing this course learn the trigonometric foundations necessary for success in Calculus and beyond. This course covers topics such as trigonometric functions and their graphs, trigonometric equations, solving triangles, polar coordinates, and includes an introduction to vectors.
Prerequisite: MTH 21 or MTH 31 or MTH 31S or an appropriate skill level demonstrated through the Mathematics Assessment Process.
Discipline:
Mathematics*