3 Credit course
Offered in Lab or Lecture Format
Prerequisite required  (MATH 1200 or Appropriate Placement-Test score)

SYLLABUS

I. RELATIONS AND FUNCTIONS

  A.  Definition and examples
  B.  Domain and range
  C.  Graphs and the vertical-line test
*D. Composition of functions and inverses of functions

II. GEOMETRIC CONCEPTS

A. Definition of angle
B. Degree measure
C. Description of various triangles
D. Pythagorean Theorem
E. Properties of 45-45-90 and 30-60-90 degree triangles (derivation)
F. Derivation of the distance formula
G. Definition of circle and parts of a circle
H. Definition of pi
I. Radian measure

III. CIRCULAR FUNCTIONS

A. Definitions
        1. Unit circle
        2. P(2 )
B. Derivingand,then,and

IV. TRIGONOMETRIC FUNCTIONS

A. Definition of the basic functions
B. Solving for trigonometric functions of angles
        1. Exact values for angles indicated in III B
        2. Calculator values for any angle
C.    Solving for the angle (general solution)
        1.     Exact values for angles indicated in III B
        2.     Calculator values for any angle

V. IDENTITIES

A. Derivation of the basic trigonometric identities
        1. Reciprocal identities
        2. Pythagorean identities
        3. Ratio identities
B. Using the basic identities and the definition of P(2 ) to prove new identities (such as sin(-2 ) = -sin(2 ))
C. Sine, cosine, and tangent of the sum or difference of two angles (no derivation)
        1. Numerical examples
        2. Use in proving other identities
D. Double-angle and half-angle formulas (no derivation)
        1. Numerical examples
        2. Use in proving other identities

VI. TRIGONOMETRIC EQUATIONS (USING IDENTITIES DESCRIBED IN V)

A. Solutions with restricted domains
B. General solutions

VII. SOLVING TRIANGLES

A. Right triangles
B. Oblique triangles
        1. Law of sines (*derivation)
        2. Law of cosines (*derivation)
C.    Vectors
        1.     Vector addition by using horizontal and vertical components
        2.     Vector addition by using right or oblique triangles
D.    Word problems

VIII. GRAPHS OF THE TRIGONOMETRIC FUNCTIONS

A. y = a sin (bx+c) +d, y = a cos (bx+c) +d
B. y = tan (x), y = csc (x), y = sec (x), y = cot (x)

IX. INVERSES OF TRIGONOMETRIC FUNCTIONS

A. Definitions and examples
B. Graphing inverses of y = sin (x), y = cos (x), y = tan (x)
C. Notation for inverses of trigonometric functions
D. Restricting the domain for sine, cosine and tangent so that their inverses will be functions
E. Evaluating the principal inverses of sine, cosine, and tangent

X. APPLICATIONS

A. Areas of sectors and segments of circles
B. Arc length
C. Angular velocity

 *Optional

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