Chabot College
Fall 2008
Course Outline for Mathematics 37
TRIGONOMETRY WITH AN EMPHASIS ON ITS GEOMETRIC FOUNDATIONS
Catalog Description:
37 - Trigonometry with an Emphasis on its Geometric Foundations
5 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: Mathematics 55, 55L or
55B (completed with a grade of C or higher) or an appropriate skill level demonstrated through the
Mathematics Assessment process. May not receive credit if Mathematics 36 has been completed.
5 hours
[Typical contact hours: 87.5]
Prerequisite Skills:
Before entering the course the student should be able to:
1.
2.
3.
4.
5.
6.
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8.
9.
10.
11.
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16.
perform basic operations on complex numbers;
solve quadratic equations by factoring, completing the square, and quadratic formula;
find complex roots of a quadratic equation;
sketch the graphs of functions and relations:
a.
algebraic, including polynomial and rational
b.
logarithmic
c.
exponential
d.
circles;
find and sketch inverse functions;
perform function composition;
solve exponential and logarithmic equations;
apply the concepts of logarithmic and exponential functions;
solve systems of linear equations in three unknowns using elimination and substitution;
apply the properties of and perform operations with radicals;
apply the properties of and perform operations with rational exponents;
solve equations and inequalities involving absolute values;
solve equations involving radicals;
graph linear inequalities in two variables;
find the distance between two points;
find the midpoint of a line segment.
Expected Outcomes for Students:
Upon the completion of the 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
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;
angles,
Chabot College
Course Outline for Mathematics 37, page 2
Fall 2008
9.
10.
11.
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16.
use the law of sines and the law of cosines to solve oblique triangles;
graph trigonometric functions;
graph the inverse sine, inverse cosine, and inverse tangent functions;
convert between polar coordinate system and rectangular coordinate system;
graph polar equations;
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;
use definitions of the items in (8), along with postulates and theorems about them, together with
undefined terms, to prove geometric theorems, both synthetically and analytically; and both
directly and indirectly;
compute areas and volumes of geometric figures.
Course Content:
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Trigonometric functions
Trigonometric equations
Trigonometric formulas and identities
The graphs of trigonometric functions and their inverses
Polar coordinates
Solution of triangles and related problems
Nature of an axiomatic system
Points, lines, planes, segments, rays, angles
Radian measure
Converse, inverse, contrapositive
Midpoint of a segment, bisector of a segment, bisector of an angle
Congruence (with related constructions) and similarity of triangles
Properties of triangles
Parallels and perpendiculars
Coordinate geometry
Properties of polygons
Areas of polygons, volumes and surface areas of polyhedra
Area and circumference of circle: volumes and surface areas of cylinders, cones, and spheres
Proofs of geometric theorems
Method of Presentation:
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2.
3.
Lectures
Group discussions
Problem solving sessions
Assignments and Methods of Evaluating Student Progress:
1.
2.
Typical Assignments
a. Read section 3.1 in your text. Do exercises 1 – 13 odd, 15 – 20 all, and 27.
b. Use the unit circles on a rectangular grid system to find values of sin x for every angle that is
a multiple of π/6 for the angles between 0 and 2π. Using those values, draw the graph of
y = sin x.
Methods of Evaluation Student Progress
a. Homework
b. Quizzes
c. Midterms
d. Final Examination
Chabot College
Course Outline for Mathematics 37, page 3
Fall 2008
Textbook(s) (Typical):
Analytic Trigonometry with Applications, Barnett/Ziegler/Byleen, Brooks/Cole Publishing Co.
2006
College Geometry A Problem Solving Approach with Applications, Masser/Tempe/Maurer,
Pearson/Prentice Hall, 2008
Special Student Materials:
Scientific calculator, ruler, and compass
Revised: CSS 9-17-07