RANGER COLLEGE

Math 1316 Plane Trigonometry

Master Syllabus

 

PREPARED BY: Dr. John Gresham 

254-647-3234 x 216

jgresham@rangercollege.edu

http://www.rangercollege.edu/math

 

COURSE DESCRIPTION: Angles and coordinates, trigonometric functions, solution of triangles, reduction theorems and formulas, identities, conditional equations, logarithms, and inverse trigonometric functions. Use of hand-held calculators in solving application problems.

 

PREREQUISITES: College Algebra (Math 1314) or concurrent enrollment

 

TEXT: Trigonometry, 8th Edition by Lial, et al

 

OTHER REQUIRED MATERIALS: graphing calculator (TI-83, 84, 85 or 86 strongly recommended), graph paper.

 

COURSE CREDIT: 3 semester hoursó3 lecture hours per week

 

INSTRUCTIONAL METHODS: Lecture supplemented by graphing calculator and computer presentations.

 

EXEMPLARY OBJECTIVES SUPPORTED BY THIS COURSE

M1. To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world problems

M2. To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically

M3. To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments

M4. To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results

M5. To interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them

M6.  To recognize the limitations of mathematical and statistical models

M7.  To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines

 

PLANE TRIGONOMETRY COURSE OBJECTIVES: To be able to demonstrate these skills in writing:

1. Solving triangles and application problems using trig functions (M1, M2)

2. Using a hand‑held calculator to solve trig problems (M4)

3. Proving trigonometric identities (M3)

4. Converting between radian and degree measure. Solving applications of radian measure (M2)

5. Using trig formulas to simplify expressions and solve trig equations (M1, M3)

6. Graphing trig functions in rectangular and polar form (M5, M6)

7. Simplifying logarithmic expressions and solving logarithmic equations (M2, M4)

8. Using the trig form of complex numbers to solve problems (M1, M7)

 

COURSE CALENDAR FOR MATH 1316 (subject to change)

 

 

Week††† Section(s) †††† Topic††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† Problem List††††††††††

1††††††††††††† 1.1†††††††††††† Angles.......................................................................... 7, 21, 27, 33, 73, 79

††††††††††††††† 1.2†††††††††††† Angle Relationships & Similar Triangles................ 5, 9, 13, 35, 43, 51, 69

††††††††††††††† 1.3†††††††††††† Definitions of the Trig Functions............................. 5, 9, 11, 37, 41, 47, 55

††††††††††††††† 1.4†††††††††††† Using the definitions of the trig functions............. 5, 11, 19, 23, 29, 39, 51-61 odd, 65,81

2††††††††††††† 1.4†††††††††††† (cont)

††††††††††††††† 2.1†††††††††††† Trig functions of acute angles.................................. 1, 5-11, 17, 29-36, 60

††††††††††††††† 2.2†††††††††††† Trig functions of non-acute angles......................... 1-6, 11, 13, 18, 19, 38, 41, 61

††††††††††††††† 2.3†††††††††††† Finding trig functions values with a calculator...... 5,6,34

3††††††††††††† 2.4†††††††††††† Solving right triangles................................................ 9,10,26,36

††††††††††††††† 2.5†††††††††††† Applications of right triangles.................................. 12, 16, 24

††††††††††††††† 3.1†††††††††††† Radian measure........................................................... 6, 9, 14, 22, 25, 26, 40, 52

††††††††††††††† 3.2†††††††††††† Applications of radian measure................................ 10, 14, 26, 42

4††††††††††††† TEST #1 (Ch 1-2)

††††††††††††††† 3.3†††††††††††† Circular functions of real numbers........................... 1, 8, 23, 30, 50, 55

††††††††††††††† 3.4†††††††††††† Linear and angular velocity....................................... 8, 32, 38, 44

5††††††††††††† 4.1†††††††††††† Graphs of sine and cosine functions....................... 1-8, 13, 24, 29

††††††††††††††† 4.2†††††††††††† Translating graphs of sinusoids.............................. 1-12, 22, 32

††††††††††††††† 4.3†††††††††††† Graphs of other circular functions........................... 1-6, 22

6††††††††††††† 5.1†††††††††††† Fundamental Identities.............................................. 28, 29-38

††††††††††††††† 5.2†††††††††††† Verifying Trig Identities............................................. 34, 50

††††††††††††††† TEST #2 (Ch 3-4)

7††††††††††††† 5.3†††††††††††† Sum and difference identities for cosine................. 1-4, 6, 16, 30, 34, 50

††††††††††††††† 5.4†††††††††††† Sum and difference identities for sin and tan......... 4, 6, 8, 12, 15, 18, 28, 42

††††††††††††††† 5.5†††††††††††† Double-angle identities.............................................. 1-6, 8, 12, 18, 20, 40

††††††††††††††† 5.6†††††††††††† Half-angle identities................................................... 5-10, 16, 21, 22, 34, 38

8††††††††††††† 6.1†††††††††††† Inverse trig functions................................................. 14, 16, 18, 20, 23, 24, 64, 68, 88

††††††††††††††† 6.2†††††††††††† Trig equations............................................................. 12, 16, 22, 30, 40, 46

9††††††††††††† 6.3†††††††††††† Trig equations II......................................................... 8, 18, 30, 32

††††††††††††††† 6.4†††††††††††† Equations with inverse trig functions..................... 6, 20, 24, 28, 36

10††††††††††† 7.1†††††††††††† Oblique triangles and the Law of Sines................... 8, 12, 18, 26, 44

††††††††††††††† TEST #3 (Ch 5-6)

11††††††††††† 7.2†††††††††††† Ambiguous case of the Law of Sines...................... 18, 22, 30, 20 solve triangle ABC

††††††††††††††† 7.3†††††††††††† Law of Cosines............................................................ 20, 26, 54, 68

12††††††††††† 7.4†††††††††††† Vectors and the Dot Product.................................... 10, 22, 24, 33, 38, 60, 72, 78, 54 find magnitude, direction of resultant

††††††††††††††† 7.5†††††††††††† Applications of vectors............................................. 6, 8, 24, 26

††††††††††††††† 8.1†††††††††††† Complex numbers........................................................ 28, 50, 60, 90

13††††††††††† 8.2†††††††††††† Trig form of complex numbers.................................. 24, 26, 32, 38, 42, 46, 48, 50

††††††††††††††† 8.3†††††††††††† Product and quotient theorems................................ 4, 8, 10, 14, 16, 18, 20, 30

† ††††††††††††† 8.4†††††††††††† Powers and roots of complex numbers.................... 6, 8, 12, 18, 24

14††††††††††† 8.5†††††††††††† Polar equations and graphs...................................... 4, 18, 37-40, 44, 56

††††††††††††††† 8.6†††††††††††† Parametric equations.................................................. 1-4, 12, 14, 40

15††††††††††† TEST #4 (Ch 7-8)

††††††††††††††† Review †††

16††††††† FINAL EXAM††††††††††† Time of Final TBA