Course Objectives :

• To facilitate a thorough understanding of the Plane Trigonometry, Spherical Trigonometry and its application/use at different places in nautical studies.
• Utilise problem solving skills in a variety of theoretical and practical situations.
• To understand the applications and fundamentals of plane & spherical trigonometry in nautical science.
• A student successfully completing the program of study will have acquired subject knowledge and understanding as well as skill and other attributes.
• Student will be regularly assessed through Assignments, Practical, Exercises, Interaction, Group Discussion, Tests, Etc. during the course period.

Course Outcomes :

After completion of the course students are expected to be able to:

• Students should understand the spherical trigonometry and apply it properly.
• To understand the applications of fundamentals of plane & spherical trigonometry in nautical science.
• Utilise problem solving skills in a variety of theoretical and practical situations.
• To understand the applications and fundamentals of plane & spherical trigonometry in nautical science.
• Utilise problem solving skills in a variety of theoretical and practical situations.

Course Syllabus :

Course content

Module I:                                                                                                       

• Plane Trigonometry Fundamental.
• Spherical Trigonometry fundamentals; Great Circle, Small Circle, Spherical angles, Spherical Triangles,
• Properties of Great Circle, small Circle and spherical Triangle,
• Spherical Excess, Sine, Cosine formulae, Versine formula, Haversine formula and its advantage over the sine cosine formula,
• Definitions and Properties of Right angle Spherical Triangle, Quadrantal Spherical Triangle, Polar Spherical Triangle,
• Napier’s Rules for Circular Parts of Right angle and Quadrantal Spherical Triangles.

Module II  :                                                                                                      

 Concepts of Radian and Degrees, Trigonometric functions sine, cosine, tangent and corresponding reciprocal ratios, bisects, Acute, obtuse and reflex angles and Isosceles triangle, equilateral, scalene triangle, right angled triangle, properties of similar and congruent Triangles, Pythagoras Theorem.

Reference Books:

1. Capt. H. Subramanian , “Spherical Trigonometry”, BOOK 8 , Vijaya Publications, Reprint Edition, 2011
2. B.S. Grewal, “Higher Engineering Mathematics”, Khanna Publications , 43rd Edition, 2013
3. Dr. P.R. Vittal , “Allied Mathematics”, Margham Publications, Chennai, Reprint Edition, 2011

REFERENCE BOOKS:

1. Graham Lawler MA, “Understanding Maths”, Viva Study Mates Publishers, Fourth Edition, 2011
2. Capt. G.E. Earl, Capt. D.M. Robinson , “Munro’s Mathematics for Deck Officers”, Glasgow : Brown, Son & Ferguson, Reprint Edition, 2007
3. Blanche, Capt A.G, “Norie’s Nautical Tables”, Blance & Wilson Publications, Revised Edition, 2007

Session Plan :

Session 1

Detail instruction regarding the syllabus, curriculum and use of spherical trigonometry in shipping.

Session 2

Detail instruction regarding the syllabus, curriculum and use of spherical trigonometry in shipping.

Session 3

Introduction / Knowledge of Plane Trigonometry

Session 4

Knowledge of Plane Trigonometry

Session 5

Spherical trigonometry fundamentals

Session 6

Spherical trigonometry fundamentals

Session 7

Great Circle, Small Circle

Session 8

Spherical Angle, Spherical Triangle, Properties of Great Circle and Small Circle

Session 9

Properties of Spherical Angle, Spherical Triangle,

Session 10

Properties of Spherical Angle, Spherical Triangle,

Session 11

Properties of Spherical Angle, Spherical Triangle,

Session 12

Simple Example, Interaction, Group Discussion

Session 13

Example, Interaction, Group Discussion

Session 14

Clearing of doubts and revision

Session 15

Examples on Spherical Triangle

Session 16

Examples on Spherical Triangle

Session 17

Right Angled Spherical Triangle

Session 18

Right Angled Spherical Triangle

Session 19

Numerical -Right Angled Spherical Triangle

Session 20

Clearing of doubts and revision

Session 21

Numerical -Right Angled Spherical Triangle

Session 22

Numerical -Right Angled Spherical Triangle

Session 23

Numerical -Right Angled Spherical Triangle

Session 24

Numerical -Right Angled Spherical Triangle

Session 25

Clearing of doubts and revision

Session 26

Quadrantal Spherical Triangle

Session 27

Quadrantal Spherical Triangle

Session 28

Quadrantal Spherical Triangle

Session 29

Revision

Session 30

Clearing of doubts and revision

Session 31

POLAR SPHERICAL TRIANGLE

Session 32

POLAR SPHERICAL TRIANGLE

Session 33

POLAR SPHERICAL TRIANGLE

Session 34

Clearing of doubts and revision,

Session 35

Trigonometry functions, Sine, Cosine, tangent, Haversine formulae, Radian and Degrees.

Session 36

Bisect, Acute, Obtuse, Reflex Angles, Isosceles,

Session 37

Equilateral, Scalene, Similar, Congruent, Symmetrical Triangles.

Session 38

Pythagoras Theorem, Supplemental Theorem

Session 39

Revision / Doubt Clearance

Session 40

Revision / Doubt Clearance