Plane+Trigonometry

COURSE SYLLABUS IN MATH 105

Subject Code: **MATHEMATICS 105** Credit: **3 units** Subject Description: **Plane Trigonometry** Intended for: **General Education Curriculum**

**DESCRIPTION: **

This course aims to develop students’ understanding of the fundamentals of trigonometric functions: angles, solution of triangles, periodic phenomenon and their applications. The course extends to include analytical trigonometry and applications of trigonometry to navigation. The use of graphing calculators and computer algebra system is highly encouraged.

**GENERAL OBJECTIVES: **

Apply the basic concept of exponential and logarithmic functions, trigonometric functions and solution of triangles in practical or real life situations and highly specialized areas as engineering, architecture, surveying, navigation and the like. **SPECIFIC OBJECTIVES: **
 * 1) Define trigonometric terms and symbols;
 * 2) Solve right and oblique triangles;
 * 3) Solve practical and workshop related problems
 * 4) Prove trigonometric identities; and
 * 5) Apply logarithm in logarithmic and exponential expressions.

**COURSE OUTLINE: **

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">Chapter I - The Trigonometric Functions (12 hrs) ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.1. Introduction <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.2. Directed Line Segments <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.3. Angles <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.4. The Pythagorean Theorem <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.5. The Rectangular Coordinate System <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.6. The Distance Formula <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.7. Standard Position of an Angle <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.8. Definition of the Trigonometric Functions of Any Angle in Standard Position <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.9. Algebraic Signs of the Trigonometric Functions <span style="font-family: 'Franklin Gothic Book',sans-serif;">1.10. Functions of 30 ° <span style="font-family: 'Franklin Gothic Book',sans-serif;">, 45 ° <span style="font-family: 'Franklin Gothic Book',sans-serif;"> and their Multiples <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.11. Functions of Quadrantal Angles

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">Chapter II - Circular Functions (9 hrs) ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.1. Equations of a Circle <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.2. Relations Between Degree and Radian Measure <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.3. Central Angle and Arc Length <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.4. Basic Circular Functions

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">Chapter III - Trigonometric Ratios and Solutions of Right Triangle Trigonometric Ratios (12 hrs) ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">3.1. Solutions of Right Triangle <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">3.2. Angles of Elevation and Depression <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">3.3. Bearings

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">Chapter IV - Fundamental Identities (9 hrs) ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.1. Introduction <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.2. The Eight Identities <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.3. Changing the Form of a Trigonometric Expression <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.4. Proving Identities

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">Chapter V - Solutions of Oblique Triangle (12 hrs) ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">5.1. Definitions and Forms of Oblique Triangle <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">5.2. Conditions that Determine a Triangle <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">5.3. The Sine Law <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">5.4. The Cosine Law

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">Chapter VI - The Logarithmic and Exponential Functions ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">6.1. Logarithmic and Exponential Form <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">6.2. Properties of Logarithm <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">6.3. Common Logarithm and Antilogarithm <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">6.4. Exponential and Logarithmic Functions

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">METHODS OF TEACHING ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Classroom discussions, oral participation, seatwork and boardwork will be the primary means of classroom instruction for this course.

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">COURSE REQUIREMENTS ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Quizzes, unit test, recitation, activities and term examinations shall be among the requirements of this course. The date of submission will be announce by the instructor.

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">CRITERIA FOR GRADING ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">The following shall be used as the basis for giving grades.

**<span style="font-family: 'Franklin Gothic Book',sans-serif;"> Class Standing 70% ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Quizzes 30% <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Attendance/Recitation 20% <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Projects/Assignments 20% **<span style="font-family: 'Franklin Gothic Book',sans-serif;">Term Examination __30%__ ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">100%

<span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">The final grade will be computed based on the 50-50 policy (50% of the Midterm + 50% of the tentative final grade)

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">REFERENCES: **
 * 1) <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">Barcelon Dolores G., et al. Plane Trigonometry. 2003.
 * 2) <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">Lumabas, Rogelio S. Plane Trigonometry. 1997.
 * 3) <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">Nocon, Ferdinand P. Simplified Trigonometry. 1998.
 * 4) <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">Nues, Cleofe T . & Ymas, Sergio E. Plane Trigonometry. 1998.
 * 5) <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Reyes, Fe. N., et al. Trigonometry. 2000