# Trigonometry

**I. Course Objectives**

Study of Degree Radian measure; right and oblique triangles; vector
applications; graph of

trig functions; graph of inverse trig functions; identities; conditional trig
equations; inverse

function; and unit circle.

**II. Topics to Be Studied
How will course objectives be met?**

I. Review of Algebraic Concepts

Real numbers

Directed lines and segments

Distance formula

Functions and graphs

II. The Trigonometric Functions

Angles and units of measure

Definition of sine, cosine and tangent, (ie sin

Cosecant, secant and cotangent functions as reciprocals

Value, the trigonometric functions for special angles (30•,• 60•,•45•,• quadrantal angles)

Circular definition of the trigonometric functions (ie, the wrapping function)

III. Triangle and Tables of Trigonometric Functions

Interpolation - Students may use a calculator to solve the triangle problems

Right triangle problems

Applications of right triangles

Oblique triangles

Ambiguous case

Law of sines and law of cosines

IV. Vectors and Applications

Introduction - components and resolution

Applications - Inclined plane

Equilibrium - wind velocity and displacement aboard ships and airplanes

V. Trigonometric Identities

Ratio identities - Pathogren identities and reciprocal identities

Proving identities

Cosine, sine and tangent of the sum and difference of two angles

Double angle formulas

Half angle formulas

Product and sum formulas

Students are expected to be able to solve a large assortment of trig identities

VI. Graphical Representation of the Trigonometric Functions

Periods of trigonometric functions

Graph the trigonometric functions

Graphing general cases: y = A sin (Bx + C), y = A cos(Bx + C), y = A tan(Bx + C),

y = A cot(Bx + C), y = A sec(Bx + C) and y = A csc(Bx + C)

VII. Trigonometric Equations and Inverse Functions

Solving conditional trigonometric equations

Inverse of a function

Inverse of the trigonometric functions

Solving inverse trigonometric equations

VIII. Optional Topics

Graphing y = A sin(Bx + C) + D cos(Ex + F) by addition of ordinates

The Scaler (inner product)

Complex Numbers

Logaritims of Trigonometric Functions

Area of triangle

S = bc sin A

**III. Special Projects to Be Included in Course**

Research papers

Surveys

Other

Reports

Annotated bibliographies

Research papers

Surveys

Other

Reports

Annotated bibliographies

**IV. Methods of Student Evaluation**

Tests (how many? how often? what type?)

Quizzes

Oral Presentations

Written Papers

Laboratory Activities

Clinical Experiences

Tests (how many? how often? what type?)

Quizzes

Oral Presentations

Written Papers

Laboratory Activities

Clinical Experiences

3 to 6 Exams - scheduled throughout the semester

Objective Exams

Comprehensive Final Exam

**V. Assessment of Outcomes**

What measurements will be used to demonstrate that outcomes have been reached?

(Refers to class as a whole, not individual students.)

What measurements will be used to demonstrate that outcomes have been reached?

(Refers to class as a whole, not individual students.)

**VI. Other Information**

What additional information will help to clarify the course?

What additional information will help to clarify the course?

Prerequisites: Math 114, or consent of instructor, or satisfactory score on Math Form C

Placement test, Reading 079