COLLEGE OF SCIENCESecond Floor, ST Building 900 San Marcelino Street, Ermita, Manila 1000 Phone (632) 524.20.11 local 222

COURSE SYLLABUS1. Course Title:PLANE AND SPHERICAL TRIGONOMETRY2. Course Description: Plane and Spherical Trigonometry is a basic course for engineering students. This course aims to develop students understanding of trigonometric functions defined for any angle as well as circular functions; identities and equations; solutions of triangles; law of cosines; law of sines; inverse trigonometric functions; graphs of trigonometric functions; exponential and logarithmic functions; application of Napiers rules of spherical trigonometry; terrestrial sphere; geographical coordinates and distances; meridians; and navigation.

3. Course Code: MH112C4. Pre-requisites:None5. Number of Units:36. Number of Hours per week: 3 hours per week7. Course Objectives and Relationship to Program OutcomesRELATIONSHIP OF THE LEARNING COMPETENCIES TO THE PROGRAM OUTCOMESPROGRAM OUTCOMES

Course Objectives:At the end of the semester, the students must be able to distinguish the units of angular measurements, the degree and radian units. Apply correct formulas in computing distances and angular measures encountered in real-life exposures and in the field of professional practice. Obtain the necessary knowledge, relevance, and application of formulas encountered in the physical sciences. Acquire the basic knowledge of spherical trigonometry as applied in the field of navigation.An ability to apply knowledge of mathematics, and engineering sciences appropriate to the field of practiceAn ability to recognize, formulate, and solve engineering problems

Specific Objectives:1. Define plane trigonometry, spherical triangle, degree and radian unit, angle, right triangle, Pythagorean theorem, angular speed, domain and range, the six trigonometric functions and their inverses, Napiers Rules, meridian, Greenwich Meridian Time (GMT), geographical coordinates, nautical mile, and speed in knot unit .II

2. Perform solution of right triangles and oblique triangles using special angles, using scientific calculator, using law of sines and cosines, proving identities, solutions of inverses, graphing of trigonometric functions and their inverses, solution of spherical triangles using Napiers rules, locating a point on earths surface using geographical coordinates, solution of distances between cities . II

3. Identify different types of triangles, trigonometric functions and their inverses, trigonometric identities, domain and range, graphs of trigonometric functions, and location of cities by geographical coordinates. II

4. Apply law of sines and cosines in solving triangles, inverses in finding angular values, apply basic identities in proving equalities of trigonometric expressions, Napiers rules in solving spherical triangles, geographical coordinates in locating a point (city)on the earths surface, laws of cosines in solving distances between cities. II

5. Analyze word problems by determining the given data, recognizing realistic values, accurate sketch of the problem, using appropriate theorems and trigonometric laws.II

6. Search for alternative solution(s), and verifying realistic values.II

8. Course CoverageWeekLearning ObjectivesLearning Content/TopicsLearning Tasks Assessment

1st

Identify the classification of angles and triangles. Differentiate degree from radian measures. Convert between degree and radian measures. Angles, triangles and their classifications. Angle measure and sector of a circle1. Degree unit2. Radian unit3. Conversions Conversion of units using Ratio and Proportion method.Demo/PresentationLecture/Discussion

Graded AssignmentsGraded Boardwork

2nd Solve the area of a sector of a circle. Compare between linear and angular speed from circular motion. State the Pythagorean theorem verbally and mathematically. Apply the theorem. Solve missing side using the theorem. Arc length Area of a sector of a circle. Angular and linear speed. Right triangle trigonometry1. Parts of a right triangle2. Pythagorean theorem3. Pythagorean triple4. Historical account (optional)Demo/PresentationLecture/DiscussionExcerpts from past engineering board exam problems.

Graded AssignmentsGraded Boardwork

3rd Define and differentiate angle of elevation and depression. Enumerate and define:1. The six ratios2. Reciprocal and complementary functions Obtain values from special angles. Solve right triangle problems. The six trigonometric ratios Reciprocal and complementary function of acute angle Functions of special angles 30. Angles of elevation and depression. Solution of right triangles.

Demo/PresentationLecture/Discussion

Graded Seatworks

Long Quiz

4th Apply right triangle, and angles of elevation and depression to real-life cases. Define/identify:1. Coterminal angles2. Quadrantal angles3. Reference angle of a general angle Applications of right triangle. Functions of a general angle.1. Angles as to direction of rotation.2. Coterminal and quadrantal angles.3. Definition of six trigo function of a general angle.4. Reference angle and reduction formulas.

Lecture/Discussion

Graded AssignmentsGraded Boardworks

5th Define/identify:1. Trigonometric function using unit circle approach.2. Finding exact values using the unit circle.3. Domain and range.4. Odd and even properties. Unit circle and trigonometric functions Domain and range of periodic functions. Even and odd properties of periodic functions.

Demo/PresentationLecture/Discussion

Long Quiz

6th Determine amplitude and periods of periodic functions. Obtain the ability to graph accurately trigonometric functions. Graphs of trigonometric functions.

Demo/PresentationLecture/DiscussionPeer DiscussionPrelimExam

7th Define a trigonometric identity. State and write correctly the fundamental identities. Obtain the skills in simplifying trigonometric expressions and proving equations of identities.

Fundamental identities:1. Reciprocal identities2. Quotient identities3. Pythagorean identities4. Cofunction identities Simplifying trigonometric expressions. Proving identities.Lecture/DiscussionInternet searchPeer DiscussionGraded SeatworkLong Quiz

8th Apply correctly and obtain skills on the following identities::1. Sum and Difference2. Double and Half-Angle 3. Product-to Sum and Sum-to-Product Multiple angle identities1. Sum and difference formulas2. Double and half-angle formulas3. Product-to-Sum and Sum-to-Product formulas Lecture/DiscussionInternet search.Graded AssignmentsGraded SeatworksGraded Boardworks

9th Define the six inverse trigonometric functions. Solve angle values using the inverse. Recognize the domain and range of inverse function. Obtain skills in graphing inverse functions. Inverse trigonometric functions Definitions Domain and range properties Graphs of the inverse trigonometric functions

Lecture/Discussion

Internet search

Graded AssignmentGraded Seatwork

10th Obtain the skills of using calculator in verifying values obtained from inverse quantities. Solving angle valueswith the use of calculator in degree and radian mode.Demo/DiscussionPeer DiscussionGraded AssignmentGraded Seatwork

11th Obtain the skills in solving trigonometric equations. Recognize between principal value and general solution. Trigonometric equations Principal value and general solution Solving trigonometric equations by:1. Factoring2. Quadratic formula3. IdentitiesLecture/DiscussionGroup Activity

Graded Board work

Long Quiz

12th Solve oblique triangle using:1. Law of sines2. Law of cosines Solve areas of triangles Apply solutions of oblique triangles in real-life cases. Solutions of oblique triangles. Applications of oblique triangles. Real-life problemsLecture/DiscussionInternet searchExcerpts from past engineering board exam problems.Midterm Exam

13th Define spherical triangle Recognize the difference between angle and sides of a spherical triangle. Recognize:1. Dihedral angle2. Polar triangle3. Quadrantal triangle Spherical TrigonometryDefinition of:1. Spherical trigonometry2. Sides and angles3. Polar triangle4. Quadrantal triangle

Spherical Model Demo/PresentationLecture/DiscussionInternet searchGradedAssignments

Graded Seatworks

14th Solve the:1. Spherical excess2. Area of spherical triangle. Spherical excess and area of spherical triangle Lecture/DiscussionInternet searchLong Quiz

15th Define Napiers rules Apply Napiers rules in solving right spherical triangles Obtain the skills in applying Napiers rules. Napiers rules Napiers mnemonic circle Schematic triangle

Lecture/DiscussionGroup DiscussionGraded AssignmentsGraded Seatworks

16th Solve oblique spherical triangles by applying :1. Law of Cosines for Sides2. Law of Cosines for Angles Formulas for Law of Cosines for:1. Sides2. Angles

Lecture/Discussion

Long Quiz

17th

Differentiate between latitude and longitudeand its measurements. Define a meridian Identify the meridian of a point and the zero meridian. Locate a city by means of the geographical coordinates. Obtain the skills in computing the distance between cities. Application Definition of: 1. Longitude and latitude.2. Meridian3. Parallels of latitude Application of law of cosines to compute distances between cities.

Demo/Presentation Globe as a model

Lecture/DiscussionGraded Assignments

Graded Seatworks Project

18thFinal Examination

9. Course Requirements:1. Attendance2. Quizzes3. Major exams 4. Project5. Assignments6. Board work7. Seatwork

10. Grading System

REQUIREMENTSEQUIVALENT PERCENTAGE

PERIODIC EXAM30%

ASSIGNMENTS12.5%

PROJECT5%

SEATWORK/BOARDWORK12.5%

QUIZZES (minimum of 2 per grading period)40%

SEMESTRAL GRADE = 30% (Prelim) + 30% (Midterm) + 40% (Finals)

11. Contribution of Course to Meeting the requirements of curriculum

Professional Component Content

MathematicsNatural/Physical SciencesBasic Engs SciencesAlliedProfessionalNon-Technical CoursesInstitutional

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12. TEXTBOOK:Richard Aufmann, Vernon Barker and Richard Nation; College Algebra and Trigonometry; (7th Ed.) Cengage Learning Asia Pte.Ltd., Pasig City, Philippines

13. REFERENCES: . Stewart, Redin, Algebra and Trigonometry (2012) Ayres, Frank, (2009); Schaums Outlines Trigonometry; New York: McGraw-Hill Ayres, Frank, (2009); Trigonometry; Hoboken, N.J.: John Mwiley Beecher, Judith A., (2012) Algebra and Trigonometry Swokowski, Earl W., (2012) Algebra and Trigonometry with Analytic Geometry

Course Title:PLANE & SPHERICAL TRIGONOMETRYDate Effective1ST TERM 2013-2014Date Revision

JAN. 30, 2013Prepared by:OBE COMMITTEE MEMBERReviewed by:Prof. Emilia VicencioApproved by:Dr. Maria LiriaDacanayPage

Chairperson Math Dept.Dean COS7 of 7