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- MATH 1316

### MATH 1316

# Plane Trigonometry

### Math 1316

**State Approval Code:**27010153119**Semester Credit Hours:**3**Lecture Hours per Week:**3**Contact Hours per Semester:**48

### Catalog Description

Circular functions, trigonometric functions and their graphs, radian measure, inverse
trigonometric functions and their graphs, solution of triangles, vectors, complex
numbers, polar coordinates, basic and special identities.

(27010153119) (3-3-0) (Fall only)

(27010153119) (3-3-0) (Fall only)

### Prerequisites

TSIP math completed and high school Algebra II and geometry or Math 1314.

### Course Curriculum

### Basic Intellectual Compentencies in the Core Curriculum

- Critical thinking

### Perspectives in the Core Curriculum

- Use logical reasoning in problem solving.

### Core Components and Related Exemplary Educational Objectives

### Mathematics

- To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations.
- To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically.
- To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments.
- To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results.
- To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them.
- To recognize the limitations of mathematical and statistical models.
- To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines.

### Instructional Goals and Purposes

Panola College's instructional goals include 1) creating an academic atmosphere in which students may develop their intellects and skills and 2) providing courses so students may receive a certificate/an associate degree or transfer to a senior institution that offers baccalaureate degrees.

### General Course Objectives

Successful completion of this course will promote the general student learning outcomes
listed below. The student will be able

1.To apply problem-solving skills through solving application problems.

2.To demonstrate arithmetic and algebraic manipulation skills.

3.To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.

4.To construct appropriate mathematical models to solve applications.

5.To interpret and apply mathematical concepts.

6.To use multiple approaches - physical, symbolic, graphical, and verbal - to solve application problems.

1.To apply problem-solving skills through solving application problems.

2.To demonstrate arithmetic and algebraic manipulation skills.

3.To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.

4.To construct appropriate mathematical models to solve applications.

5.To interpret and apply mathematical concepts.

6.To use multiple approaches - physical, symbolic, graphical, and verbal - to solve application problems.

### Specific Course Objectives

Major Learning Objectives

Essential Competencies

Upon completion of MATH 1316, the student will be able to demonstrate:

1. Competence in relating basic components of algebra and geometry to the development of trigonometry.

2. Competence in the understanding and application of mathematical terminology associated with trigonometry.

3. Competence in the determination and evaluation of trigonometric and inverse trigonometric functions.

4. Competence in the identification and computation of circular functions and inverse circular functions.

5. Competence in converting between degree angular measure and radian measure and in evaluating functions of angles.

6. Competence in the development and interpretation of graphs.

7. Competence in the identification and application of trigonometric identities and in solving conditional trigonometric equations.

8. Competence in describing, analyzing, and computing solutions of triangles.

Page 4 of 11.

9. Competence in the applications of vectors.

10. Competence in the identification and computation of complex numbers.

11. Competence in the determination and application of polar coordinates.

Essential Competencies

Upon completion of MATH 1316, the student will be able to demonstrate:

1. Competence in relating basic components of algebra and geometry to the development of trigonometry.

2. Competence in the understanding and application of mathematical terminology associated with trigonometry.

3. Competence in the determination and evaluation of trigonometric and inverse trigonometric functions.

4. Competence in the identification and computation of circular functions and inverse circular functions.

5. Competence in converting between degree angular measure and radian measure and in evaluating functions of angles.

6. Competence in the development and interpretation of graphs.

7. Competence in the identification and application of trigonometric identities and in solving conditional trigonometric equations.

8. Competence in describing, analyzing, and computing solutions of triangles.

Page 4 of 11.

9. Competence in the applications of vectors.

10. Competence in the identification and computation of complex numbers.

11. Competence in the determination and application of polar coordinates.

### General Description of Each Lecture or Discussion

After studying the material presented in the text(s), lecture, laboratory, computer
tutorials, and other resources, the student should be able to complete all behavioral/learning
objectives listed below with a minimum competency of 70%.

1. Competence in relating basic components of algebra and geometry to the development of trigonometry.

Upon completion of this section, the student will be able to correctly

1.1. Construct a rectangular coordinate system and plot a point.

1.2. Find the length of the radius vector r.

1.3. Calculate x (or y), given y (or x) and r.

1.4. State from memory the distance formula and apply it.

2. Competence in the understanding and application of mathematical terminology associated with trigonometry.

Upon completion of this section, the student will be able to correctly

2.1. Define trigonometric angle and construct it.

2.2. Define complementary and supplementary angles and calculate the complement and supplement of angles.

2.3. Define angle in standard position and construct it.

2.4. Define coterminal angles and give examples.

2.5. Show that any point along the terminal side of X is valid in satisfying the definition.

3. Competence in the determination and evaluation of trigonometric and inverse trigonometric functions.

Upon completion of this section, the student will be able to correctly

3.1. Define the six trigonometric functions.

3.2. Determine the reciprocals of sine, cosine, and tangent.

3.3. Show that any trigonometric function of an angle is equal to the same function of all angles coterminal with it.

3.4. Find the sign of the trigonometric functions in the four quadrants.

3.5. Find the values of the trig functions of quadrantal angles 0 degrees, 90 degrees, 180 degrees, and 270 degrees.

3.6. Find the values of the trig functions for special angles using reference angles of 30 degrees, 45 degrees, and 60 degrees.

3.7. Find the values of the trig function of X given a point along the terminal side of X.

3.8. Write the six (6) trigonometric functions in terms of side opposite, side adjacent, and hypotenuse.

3.9. Write the trig functions in terms of their cofunctions and complementary angle.

3.10. Draw the special 30-60-90 degree and 45-45-90 degree right triangles, label the sides and write the values of the six trig functions.

3.11. Use the inverse trig functions to find the measurement of angles.

3.12. Solve a right triangle given two of its sides or one side and an acute angle.

3.13. Draw the angles of elevation and depression and work applications involving them.

3.14. Draw the bearing of a line and work applications.

4. Competence in the identification and computation of circular functions and inverse circular functions.

Upon completion of this section, the student will be able to correctly

4.1. Use the concept of the Unit Circle to define the six circular functions in terms of arc length, s, x, and y.

4.2. Find the arc length of a circle given a central angle and radius.

4.3. Find the area of a sector of a circle.

5. Competence in converting between degree angular measure and radian measure and in evaluating functions of angles.

Upon completion of this section, the student will be able to correctly

5.1. Change from degree measure into radian measure and visa versa.

5.2. Find the linear velocity of a point as it rotates around a circle.

5.3. Find the angular velocity of a ray as it rotates through a circle.

6. Competence in the development and interpretation of graphs.

Upon completion of this section, the student will be able to correctly

6.1. Define periodic functions and illustrate.

6.2. Use the Unit Circle to determine the variation of each of the six (6) trig functions on the interval 0 degrees < X < 360 degrees.

6.3. Determine the amplitude and period (wave length) of each trig function.

6.4. Sketch the graphs of each of the six (6) trig functions noting amplitude, change in period, phase shift, and vertical shift.

7. Competence in the identification and application of trigonometric identities and in solving conditional trigonometric equations.

Upon completion of this section, the student will be able to correctly

7.1. Write from memory the fundamental identities.

7.2. Write the six trig functions in terms of a specific trig function.

7.3. Simplify an expression using trig identities.

7.4. Prove (certain selected) identities.

7.5. Compute without use of tables or calculators and under given conditions:

(i) The Sine of the sum/difference of 2 angles.

(ii) The Cosine of the sum/difference of 2 angles.

(iii) The Tangent of the sum/difference of 2 angles.

7.6. Prove (or disprove) identities involving the Sine, Cosine, or Tangent of the sum/difference of 2 angles.

7.7. Compute without tables or calculators the Sine, Cosine, and/or Tangent of double angles and half-angles.

7.8. Prove identities using the Sine, Cosine, and Tangent of double and half-angle formulae.

7.9. Solve equations for X on the interval 0 degrees < X < 360 degrees or 0 < X < 2pi.

7.10. Recall from memory the proper quadrants where the six (6) inverse trig functions are defined.

7.11. Write the principal value range for the inverse functions.

7.12. Evaluate the value of any of the six (6) inverse trig functions which do not yield well-known angles.

7.13.Solve equations involving the six (6) inverse trigonometric functions.

7.14. Solve conditional trigonometric equations for all values of X on either of the following intervals: 0 degrees < X < 360 degrees or 0 < X < 2pi.

8. Competence in describing, analyzing, and computing solutions of triangles.

Upon completion of this section, the student will be able to correctly

8.1. Define oblique triangles.

8.2. Solve oblique triangles by

(i) Identifying the correct law to use: Law of Sines or Law of Cosines; and

(ii) Applying the Law of Sines and/or the Law of Cosines.

8.3. Calculate the area of oblique triangles.

9. Competence in the applications of vectors.

Upon completion of this section, the student will be able to correctly

9.1. Draw geometric representations of vectors.

9.2. Add and subtract vectors.

9.3. Find the magnitude of a given vector.

9.4. Represent vectors as ordered pairs.

9.5. Find the opposite of a given vector

9.6. Define the zero vector.

9.7. Define the unit vectors i and j.

9.8. Find the inner (dot) product of two given vectors.

10. Competence in the identification and computation of complex numbers.

Upon completion of this section, the student will be able to correctly

10.1. Define a complex number.

10.2. Give example of complex numbers, pure imaginary numbers, and real numbers.

10.3. Perform the four basic arithmetic operations of addition, subtraction, multiplication, and division with complex numbers using the algebraic form of the complex number.

10.4. Solve simple equations involving complex numbers.

10.5. Graph complex numbers in the complex plane.

10.6. Write a complex number in both algebraic and trigonometric form.

10.7. Multiply complex numbers in trigonometric form.

10.8. Evaluate complex numbers raised to powers using DeMoivre's Theorem.

10.9. Calculate all of the n-th roots of a complex number.

10.0. Solve equations for all roots of the variable.

11. Competence in the determination and application of polar coordinates.

Upon completion of this section, the student will be able to correctly

11.1. Define polar coordinates.

11.2.Use a graphing calculator to graph polar equations.

11.3. Convert between polar and rectangular coordinates.

1. Competence in relating basic components of algebra and geometry to the development of trigonometry.

Upon completion of this section, the student will be able to correctly

1.1. Construct a rectangular coordinate system and plot a point.

1.2. Find the length of the radius vector r.

1.3. Calculate x (or y), given y (or x) and r.

1.4. State from memory the distance formula and apply it.

2. Competence in the understanding and application of mathematical terminology associated with trigonometry.

Upon completion of this section, the student will be able to correctly

2.1. Define trigonometric angle and construct it.

2.2. Define complementary and supplementary angles and calculate the complement and supplement of angles.

2.3. Define angle in standard position and construct it.

2.4. Define coterminal angles and give examples.

2.5. Show that any point along the terminal side of X is valid in satisfying the definition.

3. Competence in the determination and evaluation of trigonometric and inverse trigonometric functions.

Upon completion of this section, the student will be able to correctly

3.1. Define the six trigonometric functions.

3.2. Determine the reciprocals of sine, cosine, and tangent.

3.3. Show that any trigonometric function of an angle is equal to the same function of all angles coterminal with it.

3.4. Find the sign of the trigonometric functions in the four quadrants.

3.5. Find the values of the trig functions of quadrantal angles 0 degrees, 90 degrees, 180 degrees, and 270 degrees.

3.6. Find the values of the trig functions for special angles using reference angles of 30 degrees, 45 degrees, and 60 degrees.

3.7. Find the values of the trig function of X given a point along the terminal side of X.

3.8. Write the six (6) trigonometric functions in terms of side opposite, side adjacent, and hypotenuse.

3.9. Write the trig functions in terms of their cofunctions and complementary angle.

3.10. Draw the special 30-60-90 degree and 45-45-90 degree right triangles, label the sides and write the values of the six trig functions.

3.11. Use the inverse trig functions to find the measurement of angles.

3.12. Solve a right triangle given two of its sides or one side and an acute angle.

3.13. Draw the angles of elevation and depression and work applications involving them.

3.14. Draw the bearing of a line and work applications.

4. Competence in the identification and computation of circular functions and inverse circular functions.

Upon completion of this section, the student will be able to correctly

4.1. Use the concept of the Unit Circle to define the six circular functions in terms of arc length, s, x, and y.

4.2. Find the arc length of a circle given a central angle and radius.

4.3. Find the area of a sector of a circle.

5. Competence in converting between degree angular measure and radian measure and in evaluating functions of angles.

Upon completion of this section, the student will be able to correctly

5.1. Change from degree measure into radian measure and visa versa.

5.2. Find the linear velocity of a point as it rotates around a circle.

5.3. Find the angular velocity of a ray as it rotates through a circle.

6. Competence in the development and interpretation of graphs.

Upon completion of this section, the student will be able to correctly

6.1. Define periodic functions and illustrate.

6.2. Use the Unit Circle to determine the variation of each of the six (6) trig functions on the interval 0 degrees < X < 360 degrees.

6.3. Determine the amplitude and period (wave length) of each trig function.

6.4. Sketch the graphs of each of the six (6) trig functions noting amplitude, change in period, phase shift, and vertical shift.

7. Competence in the identification and application of trigonometric identities and in solving conditional trigonometric equations.

Upon completion of this section, the student will be able to correctly

7.1. Write from memory the fundamental identities.

7.2. Write the six trig functions in terms of a specific trig function.

7.3. Simplify an expression using trig identities.

7.4. Prove (certain selected) identities.

7.5. Compute without use of tables or calculators and under given conditions:

(i) The Sine of the sum/difference of 2 angles.

(ii) The Cosine of the sum/difference of 2 angles.

(iii) The Tangent of the sum/difference of 2 angles.

7.6. Prove (or disprove) identities involving the Sine, Cosine, or Tangent of the sum/difference of 2 angles.

7.7. Compute without tables or calculators the Sine, Cosine, and/or Tangent of double angles and half-angles.

7.8. Prove identities using the Sine, Cosine, and Tangent of double and half-angle formulae.

7.9. Solve equations for X on the interval 0 degrees < X < 360 degrees or 0 < X < 2pi.

7.10. Recall from memory the proper quadrants where the six (6) inverse trig functions are defined.

7.11. Write the principal value range for the inverse functions.

7.12. Evaluate the value of any of the six (6) inverse trig functions which do not yield well-known angles.

7.13.Solve equations involving the six (6) inverse trigonometric functions.

7.14. Solve conditional trigonometric equations for all values of X on either of the following intervals: 0 degrees < X < 360 degrees or 0 < X < 2pi.

8. Competence in describing, analyzing, and computing solutions of triangles.

Upon completion of this section, the student will be able to correctly

8.1. Define oblique triangles.

8.2. Solve oblique triangles by

(i) Identifying the correct law to use: Law of Sines or Law of Cosines; and

(ii) Applying the Law of Sines and/or the Law of Cosines.

8.3. Calculate the area of oblique triangles.

9. Competence in the applications of vectors.

Upon completion of this section, the student will be able to correctly

9.1. Draw geometric representations of vectors.

9.2. Add and subtract vectors.

9.3. Find the magnitude of a given vector.

9.4. Represent vectors as ordered pairs.

9.5. Find the opposite of a given vector

9.6. Define the zero vector.

9.7. Define the unit vectors i and j.

9.8. Find the inner (dot) product of two given vectors.

10. Competence in the identification and computation of complex numbers.

Upon completion of this section, the student will be able to correctly

10.1. Define a complex number.

10.2. Give example of complex numbers, pure imaginary numbers, and real numbers.

10.3. Perform the four basic arithmetic operations of addition, subtraction, multiplication, and division with complex numbers using the algebraic form of the complex number.

10.4. Solve simple equations involving complex numbers.

10.5. Graph complex numbers in the complex plane.

10.6. Write a complex number in both algebraic and trigonometric form.

10.7. Multiply complex numbers in trigonometric form.

10.8. Evaluate complex numbers raised to powers using DeMoivre's Theorem.

10.9. Calculate all of the n-th roots of a complex number.

10.0. Solve equations for all roots of the variable.

11. Competence in the determination and application of polar coordinates.

Upon completion of this section, the student will be able to correctly

11.1. Define polar coordinates.

11.2.Use a graphing calculator to graph polar equations.

11.3. Convert between polar and rectangular coordinates.

### Methods of Instruction/Course Format/Delivery

Methods employed will include lecture/demonstration, discussion, problem solving,
analysis, and reading assignments. The instructor will also use Canvas for discussion,
demonstrations, and video presentation. Homework will be assigned.

### Assessment

•Attendance

•Class preparedness and participation

•Collaborative learning projects

•Exams/tests/quizzes

•Homework

•Scientific observations

•Student-teacher conferences

•Oral questioning in class

•Student presentations at the board

•Class preparedness and participation

•Collaborative learning projects

•Exams/tests/quizzes

•Homework

•Scientific observations

•Student-teacher conferences

•Oral questioning in class

•Student presentations at the board

Letter Grades for the Course will be assigned as follows:

A: 90 < Average < 100

B: 80 < Average < 90

C: 70 < Average < 80

D: 60 < Average < 70

F: 00 < Average < 60

A: 90 < Average < 100

B: 80 < Average < 90

C: 70 < Average < 80

D: 60 < Average < 70

F: 00 < Average < 60