Course Outline for Mathematics 37
Trigonometry with an Emphasis on its Geometric Foundations

Effective: Fall 2019
SLO Rev: 09/23/2016
Catalog Description:

MTH 37 - Trigonometry with an Emphasis on its Geometric Foundations

5.00 Units

Plane trigonometry, with topics from plane geometry. Contains the entire subject content of Mathematics 36. Includes circular and right triangle trigonometric functions; trigonometric equations, graphs and identities; triangle solutions. Polar coordinates. Also includes congruence, properties of polygons, parallel lines, similarity, areas, volumes, and coordinate geometry.
Prerequisite: MTH 55 or MTH 55L or MTH 55B or an appropriate skill level demonstrated through the Early Assessment Program or an appropriate skill level demonstrated through the Mathematics Assessment process. May not receive credit if Mathematics 36 has been completed.
1701.00 - Mathematics, General
Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 5.00 90.00 180.00 270.00
Total 5.00 90.00 180.00 270.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. identify and use the trigonometric ratios in problem solving;
  2. use radian measure;
  3. define trigonometric functions in terms of the right triangle and the unit circle;
  4. write down from memory the values of sine, cosine, and tangent functions of standard angles, both in degree and radian measure;
  5. write down from memory the Pythagorean identities, reciprocal identities, double angle formulas for sine and cosine, and sum and difference formulas for the sine and cosine;
  6. prove trigonometric identities;
  7. use trigonometric formulas;
  8. solve trigonometric equations with multiple angles over different intervals;
  9. use the law of sines and the law of cosines to solve oblique triangles;
  10. graph trigonometric functions;
  11. graph the inverse sine, inverse cosine, and inverse tangent functions;
  12. convert between polar coordinate system and rectangular coordinate system;
  13. graph polar equations;
  14. define and/or illustrate: segment, ray, angle, midpoint of a segment, bisector of an angle or segment, types of triangles and other polygons, congruence and similarity of triangles, perpendicular and parallel lines;
  15. use definitions of the items in (14), along with postulates and theorems about them, together with undefined terms, to prove geometric theorems, both synthetically and analytically; and both directly and indirectly;
  16. compute areas and volumes of geometric figures.
Course Content:
  1. Trigonometric functions
  2. Trigonometric equations
  3. Trigonometric formulas and identities
  4. The graphs of trigonometric functions and their inverses
  5. Polar coordinates
  6. Solution of triangles and related problems
  7. Nature of an axiomatic system
  8. Points, lines, planes, segments, rays, angles
  9. Radian measure
  10. Converse, inverse, contrapositive 
  11. Midpoint of a segment, bisector of a segment, bisector of an angle
  12. Congruence (with related constructions) and similarity of triangles
  13. Properties of triangles
  14. Parallels and perpendiculars
  15. Coordinate geometry
  16. Properties of polygons
  17. Areas of polygons, volumes and surface areas of polyhedra
  18. Area and circumference of circle: volumes and surface areas of cylinders, cones, and spheres
  19. Proofs of geometric theorems
Methods of Instruction:
  1. Lecture/Discussion
  2. Distance Education
  3. Problem solving sessions
Assignments and Methods of Evaluating Student Progress:
  1. Read section 3.1 in your text. Do exercises 1 – 13 odd, 15 – 20 all, and 27.
  2. Use the unit circles on a rectangular grid system to find values of sin x for every angle that is a multiple of ?/6 for the angles between 0 and 2?. Using those values, draw the graph of y = sin x.
  1. Quizzes
  2. Home Work
  3. Exams/Tests
  4. Final Examination
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. Dugopolski (2015). Trigonometry (4 th). Pearson Publishing.
  2. Alexander, D., Koeberlein, G (2015). Elementary Geometry for College Students (6th). Cengage.
  • Scientific calculator
  • Ruler
  • Compass
Abbreviated Class Schedule Description:
Plane trigonometry, with topics from plane geometry. Contains the entire subject content of Mathematics 36. Includes circular and right triangle trigonometric functions; trigonometric equations, graphs and identities; triangle solutions. Polar coordinates. Also includes congruence, properties of polygons, parallel lines, similarity, areas, volumes, and coordinate geometry.
Prerequisite: MTH 55 or MTH 55L or MTH 55B or an appropriate skill level demonstrated through the Early Assessment Program or an appropriate skill level demonstrated through the Mathematics Assessment process. May not receive credit if Mathematics 36 has been completed.
Discipline:
Mathematics*