12/21/2024 8:51:30 AM	APTECH 90B Course Outline as of Fall 1992	Changed Course
CATALOG INFORMATION
Discipline and Nbr:  APTECH 90B	Title:  QUANT REASON/APTECH
Full Title:  Quantitative Reasoning in Applied Technology
Last Reviewed:10/17/2011

Units		Course Hours per Week			Nbr of Weeks	Course Hours Total
Maximum	3.00	Lecture Scheduled	3.00		17.5 max.	Lecture Scheduled	52.50
Minimum	3.00	Lab Scheduled	0		6 min.	Lab Scheduled	0
		Contact DHR	0			Contact DHR	0
		Contact Total	3.00			Contact Total	52.50
		Non-contact DHR	0			Non-contact DHR Total	0

Total Out of Class Hours:  105.00

Total Student Learning Hours: 157.50

Title 5 Category:  AA Degree Applicable
Grading:  Grade or P/NP
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As: 
Formerly:  CET 90B

Catalog Description:

A course in quantitative reasoning which applies trigonometry principles to problems encountered in surveying, civil engineering, construction, electronics and related engineering technologies. The areas of study are the analysis, solution and application of angle measurements and their related functions, associated graphical representations, solution to triangles, complex numbers and analytic geometry, as they are related to the trades and various technologies.

Prerequisites/Corequisites:
Course Completion of APTECH 90A ( or CET 90A) OR Completion of MATH 155 or higher (V1) OR Completion of MATH 155 or higher (V2)

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description:

A course in quantitative reasoning which applies trigonometry principles encountered in surveying, civil engineering, construction, electronics and related engineering technologies.

(Grade or P/NP)
Prerequisites:Course Completion of APTECH 90A ( or CET 90A) OR Completion of MATH 155 or higher (V1) OR Completion of MATH 155 or higher (V2)
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

Associate Degree:		Effective:	Fall 1981	Inactive:	Fall 2009
Area:	B B MC	Communication and Analytical Thinking Communication and Analytical Thinking Math Competency
CSU GE:	Transfer Area			Effective:	Inactive:
	B4	Math/Quantitative Reasoning		Fall 1991	Fall 1997
IGETC:	Transfer Area			Effective:	Inactive:
CSU Transfer:	Transferable	Effective:	Spring 1982	Inactive:	Spring 2016
UC Transfer:		Effective:		Inactive:
C-ID:

Certificate/Major Applicable: Certificate Applicable Course

COURSE CONTENT

Outcomes and Objectives:
At the conclusion of this course, the student should be able to:

The student will be able to demonstrate their knowledge of the theories,

concepts and skills used in quantitative reasoning which applies

goniometric principles to solve selected problems encountered in

surveying, civil engineering, construction, electronics and related

engineering technologies.  For example the student will be able to:

1.  State the purpose, function, and application of trigonometry

including definitions, characteristics of functions, radian and degree

measurements, and inverse functions.

2.  Demonstrate and apply Pythagorean's theorem to the laying out of a

right triangle with a tape.

3.  Demonstrate and apply trigonometry to solve right triangles including

applications to the construction trades with the determination of the

slopes of roofs and various member roof cuts.

4.  Demonstrate and apply trigonometry to solve right triangles including

applications to the construction trades with the determination of the

angles found in rafters, studs, and bracing.

5.  Demonstrate and apply trigonometry to solve right triangles including

applications to the construction trades with the determination of the

lengths of rafters.

6.  Demonstrate and apply trigonometry to solve right triangles including

applications to the construction trades with the determination of the

angles and lengths of members in trusses.

7.  Demonstrate and apply trigonometry to solve right triangles including

applications to the construction and surveying trades with the

determination of the grades of roads and railroads, general slope

measurements, and horizontal measurements taken on slopes.

8.  Demonstrate and apply trigonometric concepts of oblique triangles

to triangle solutions including right triangles and oblique triangles,

that are utilized in the construction and civil engineering technologies.

9.  Demonstrate and apply the trigonometric concepts of oblique triangles

to the Law of Sines and the Law of Cosines, that are utilized in the

construction and civil engineering technologies.

10. Demonstrate and apply the trigonometric concepts of oblique triangles

as found in the construction trades with the determination of angles and

lengths of members in trusses containing oblique triangles.

11. Demonstrate and apply the trigonometric concepts of oblique triangles

as found in the construction trades with the determination of lengths of

sides in triangular lots.

12.  Demonstrate and apply the trigonometric concepts of oblique triangles

as found in the construction trades as with the applications of vector

additions involving three vectors forming oblique triangle, as well as the

application of vector sums, angles and magnitude of force, displacement

and velocity vectors.

13. Demonstrate and apply the trigonometric concepts of oblique triangles

as found in the construction trades as with the applications of vector

addition involving three vectors forming an oblique triangle, such as

found in the application of determining the static equilibrium of cables,

beams and trusses.

14. Demonstrate and apply the trigonometric concepts of components of

vectors and vector addition found in the construction trades as with the

applications of horizontal and vertical components of forces.

15. Demonstrate and apply the trigonometric concepts of components of

vectors and vector addition found in the construction trades as with the

applications of N-S and E-W components of displacements and velocities.

16. Demonstrate and apply the trigonometric concepts of components of

vectors and vector addition found in the construction trades as with the

addition of two perpendicular forces, displacements and velocities.

17. Demonstrate and apply the trigonometric concepts of components of

vectors and vector addition found in the construction trades as with the

applications of vector addition and subtraction involving more than three

vectors such that would be found in the application of determining vector

sums, angles and magnitude of force, displacement and velocity vectors.

18. Demonstrate and apply the trigonometric concepts of components of

vectors and vector addition found in the construction trades as with the

applications in determining the static equilibrium of cables, beams and

trusses.

19. Demonstrate and apply the techniques of analytic geometry with regard

to arc lengths and areas found in the construction trades as shown with

the determination of the arc length and area of sectors.

20. Demonstrate and apply the techniques of analytic geometry with regard

to arc lengths and areas found in the construction trades as shown with

the determination of the lengths of highway curves and land areas within

higway curves.

21. Demonstrate and apply the techniques used in the graphing of trigon-

ometric functions as found in the construction, electrical and electronic

technology trades as shown with the determination of amplitude, periodic

functions, resonance, graphs of trigonometric functions, general graphing

and graphing by the addition of ordinates.

Topics and Scope

Theories, concepts and skills used in quantitative reasoning which applies

goniometric principles to solve selected problems encountered in

surveying, civil engineering, construction, electronics and related

engineering technologies.  For example the topics covered include:

1.  Application of Trigonometric Functions

   a.  application of definitions for surveying

   b.  characteristics of functions used

   c.  applications of radian and degree measurements to triangular lots

   d.  applications to right triangles as found in construction

       applications

   e.  application to the length and areas of sectors (i.e. streets and

       highway curves)

2.  Application involving Oblique Triangles

   a.  applications of trigonometric functions to similar triangles

   b.  application of oblique triangles

   c.  determination of the area of triangles

   d.  applications of the Law of Sines

   e.  applications of the Law of Cosines

   f.  ambiguous triangles and associated errors in judgment

3.  Components of Vectors and Vector Addition

   a.  definition of vectors

   b.  addition and subtraction of vectors

   c.  complex numbers

   d.  polar coordinates

4.  Applications of Arc Lengths and Areas

   a.  application to the length and areas of sectors (i.e. streets and

       highway curves)

   b.  applications of analytic geometry

   c.  applications to irregularly shaped lots

5.  Application of Sine and Cosine Graphs

   a.  genera graphing of functions and graphing by the addition of

       coordinates

   b.  analysis of amplitude

   c.  analysis of periodic function

   d.  analysis of resonance

Assignments:

Application of concepts and problem solving in the following areas:

1.  Introduction of Trigonometry (definitions, characteristics of

   functions, radian and degree measure, inverse functions, arc length

   and area of a sector). Applications include solving problems such as:

   laying out right angles using tape measure;  determining slope of

   roofs and angles of rafters;  determining the length of truss members.

2.  Graphing Trigonometric Functions (amplitude, periodic function,

   resonance, graphs of fundamental trigonometric functions, general

   graphing and graphing by addition of ordinates). Applications include

   solving problems such as:  determining the relationships found in

   inductive and capacitive circuits;  interpreting Lissajous figures;

   determining structural dampening effects through the addition of sine

   and cosine waves.

3.  Identities and Conditional Equations (fundamental identities,

   reciprocal identities, quotient identities, sign identities,

   pythagorean identities, proof, sum, and difference of angles and

   related identities, trigonometric equations and their solutions).

   Applications include solving problems such as:  determining the

   sum and difference of two angles in electronic circuit theory and wave

   mechanics;  determining harmonic dampening applied to structures;

   determining power in AC circuit by using electric power law.

4.  Triangle Solutions (right triangles, oblique triangles, Law of Sine,

   Law of Cosine, area of triangles, numerical solutions by use of

   calculators). Applications include solving problems such as:

   determining length of truss members with oblique angles;  using

   survey techniques to determine property line lengths;  determining

   vector sums, angles, and magnitude of force for problems encountered

   in construction and structures.

5.  Complex Numbers and Polar Coordinates (definitions, arithmetic of

   complex numbers, graphical representation, powers of complex numbers,

   polar form of curves, definitions of vectors, addition and subtraction

   of vectors).  Applications include solving problems such as:

   determining sum of two perpendicular forces, and the addition or

   subtraction of vectors applied to construction problems;

   determining displacements and velocities;  determining horizontal and

   vertical force components; determining N-S and E-W survey components.

6.  Analytic Geometry (applications of analytic geometry). Applications

   include solving problems such as: determining arc length and sector

   areas used in calculating highway curves and land areas within high-

   way curves;  determining the area of irregularly shaped lots.

Methods of Evaluation/Basis of Grade.

Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing.		Writing 0 - 0%
None
This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments and skill demonstrations are more appropriate for this course.
Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills.		Problem Solving 10 - 50%
Homework problems
Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams.		Skill Demonstrations 25 - 50%
Performance exams
Exams: All forms of formal testing, other than skill performance exams.		Exams 10 - 40%
QUIZZES AND TECHNICAL PROBLEMS TO SOLVE
Other: Includes any assessment tools that do not logically fit into the above categories.		Other Category 0 - 10%
ATTENDANCE AND CLASS PARTICIPATION

Representative Textbooks and Materials:

Fundamentals of Technical Mathematics, Arthus D Kramer:  Glencoe/

McGraw-Hill, 1992

Applied Trigonometry, McHale and Witzke:  Addison-Wesley, 1985

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