Course Syllabus

MATH 1060 Trigonometry

Course Description

This course will cover trigonometric functions, definitions, radian/angle measure, graphs, solving trigonometric equations, identities, vectors, Law of Sines, Law of Cosines, complex numbers, polar coordinates. Graphing calculator required.

Justification

A strong foundation in trigonometry is vital for students' future success in calculus and other science related majors. Math 1060 (as numbered) exists at all other state institutions and covers the same content.

General Education Outcomes

1. A student who completes the GE curriculum has a fundamental knowledge of human cultures and the natural world. Mathematics is the language used by many fields and almost every culture to communicate about events and processes that occur in the natural world. Much of this language is rooted in the topics covered in this course. Trigonometry is one of the most applicable maths in the world. Created/invented in the western world by the Greeks to explain and understand their planet and solar system, the opportunity students have to make connections between this field of math and its usability with their world on large and small scales is staggering. Students will demonstrate their conceptions of trigonometry and their world through group work, participation, projects, homework and/or exams.
2. A student who completes the GE curriculum can read and research effectively within disciplines. Mathematics, students must be able to carefully examine a given problem then determine and execute a plan for solving the problem. Often the information given is presented using symbols and variables the student must be able to read and interpret mathematically within the context of the given problem. This ability to read, retrieve, evaluate, interpret, and deliver mathematical information will be assessed using group work, participation, projects, homework and/or exams.
3. A student who completes the GE curriculum can draw from multiple disciplines to address complex problems. Students will develop their ability to analyze a problem, determine an appropriate approach to solve the problem, and then apply their approach to reach a reasonable solution. As they learn new skills to solve mathematical problems, they are also shown how those skills can be used to solve real life problems through a variety of application problems. Exposure to these problems allows students to see how math plays a part in everyday life. The skills developed will be necessary for the students as they continue on in their studies of the sciences. They will demonstrate competency through group work, participation, projects, homework and/or exams.
4. A student who completes the GE curriculum can reason analytically, critically, and creatively. To be able to solve a mathematical problem a student must first examine what information is given, determine what information is needed, decide what process will best fit the problem to arrive at a conclusion, and then finally decide if the answer reached is reasonable. Through this course students are taught to reason analytically, critically and creatively about different math processes and facts. Students studying trigonometry will use aspects of arithmetic, algebra, geometry, number theory and calculus to completely understand the subject and be able to use it effectively in the course and in their future studies. They will demonstrate competency through group work, participation, projects, homework and/or exams.
5. A student who completes the GE curriculum can reason quantitatively.  The ability to reason logically about quantitative values is important to this course. Homework exercises and exam problems require computational skills in a variety of theoretical and applied situations. Trigonometry lends itself to a vast array of worldwide experiences as students study the field and see and explore its applications all over the world. Students will demonstrate competency through group work, participation, projects, homework and/or exams.

General Education Knowledge Area Outcomes

1. Students will be able to use the six basic trigonometric functions appropriately, including graphing. Students will be assessed using homework, quizzes, projects, and/or exams. Students will be able to use the six basic trigonometric functions appropriately, including graphing. Students will be assessed using homework, quizzes, projects, and/or exams.
2. Convert relevant information into various mathematical forms (e.g., equations, graphs, diagrams, and tables). Students will know basic trigonometric identities and use them to verify other trigonometric identities. Students will be assessed using homework, quizzes, projects, and/or exams.
3. Demonstrate the ability to successfully complete basic calculations to solve problems. Students will be able to complete calculations with angles in both degree and radian measure, including standard trigonometric angles. Student will also be able to solve trigonometric equations including multiple angle equations. Students will be assessed using homework, quizzes, projects, and/or exams.
4. Demonstrate the ability to problem solve using quantitative literacy across multiple disciplines. Make judgments and draw appropriate conclusions based on quantitative analysis of data, recognizing the limits of this analysis. Students will be able to apply trigonometry to situations requiring the Law of Sines, Law of Cosines, and/or vectors. Students will be assessed using homework, quizzes, projects, and/or exams.
5.  Students will use trigonometric tables, graphs and equations to demonstrate solutions and reasoning to trigonometric applications. Students will be assessed using homework, quizzes, projects, and/or exams.

Student Learning Outcomes

1. Upon successful completion of this course, students will understand the use of the unit circle, basic trigonometric functions and their applications.
2. Upon successful completion of this course, students will be able to graph trigonometric functions and understand their applications.
3. Upon successful completion of this course, students will be able to use identities to prove other identities and solve for trigonometric equations.
4. Upon successful completion of this course, students will be able to solve problems related to the polor coordinate plane, equations, vectors and parametric equations.

Course Content

This course includes:*Prerequisites for trigonometry: functions, inverse functions, graphing using transformations, fractions, ratios, mathematical expression simplification, solving mathematical equations, imaginary/complex numbers.*Trigonometric functions: definitions using a unit circle, definitions using triangles, right angle applications, graphs of the trigonometric functions, and inverse trigonometric functions.*Trigonometric identities and equations: fundamental identities, Pythagorean identities, sum and difference identities, even and odd identities, cofunction identities, half angle and double angle identities, and trigonometric equations *Applications: right triangle trigonometry, law of sines and cosines, area of triangles, vectors, and complex numbersThis course supports a learning environment where perspectives are recognized, respected and encouraged. Individual instructors are encouraged to include at least one assignment (other than story problems from the book) such as projects, readings, or presentations where the students can see how the concept applies to their lives.