School

Science, Technology, Engineering and Math

Division

Mathematics

Department

Mathematics

Academic Level

Undergraduate

Course Subject

Mathematics

Course Number

112

Course Title

Trigonometry

Credit Hours

3.00

Instructor Contact Hours Per Semester

47.00 (for 15-week classes)

Student Contact Hours Per Semester

47.00 (for 15-week classes)

Grading Method

A-E

Pre-requisites

MATH-103 OR MATH-1094 OR MATH-110 with a C grade or better OR a satisfactory score on the Math placement test.

Catalog Course Description

For students in a technical or science program that requires knowledge of trigonometry. Topics include angles, right triangle trigonometry, circular functions and their graphs, trigonometric identities and equations, the Laws of Sines and Cosines, vectors, and a variety of physical applications. Course does not satisfy the MATH-175 or MATH-180 prerequisite. Requires a non-graphing scientific calculator for formal assessments and access to an online homework management system.

### Goals, Topics, and Objectives

Goal Statement

- To develop an understanding of:

a) trigonometry of angles;

b) trigonometry of triangles;

c) trigonometry of functions. - To develop skills in:

a) solving triangles;

b) proving trigonometric identities;

c) solving trigonometric equations. - To develop familiarity with mathematical and physical applications of trigonometry.
- To develop skills in the use of non-graphing scientific calculators with respect to trigonometric values.

Core Course Topics

- Angles
- Find the complement and the supplement of an angle.
- Calculate and convert angle degrees, minutes, and seconds.
- Find measures of co-terminal angles.
- Use geometric properties applying to angles.
- Solve applied problems.

- Basic Trigonometric Functions
- Define the six trigonometric functions.
- Define and use reciprocal identities.
- Define and use Pythagorean identities.
- Define and use quotient identities.
- Identify signs, domains, and ranges for trigonometric functions.

- Right Triangle Trigonometry
- Define the six trigonometric functions based on right triangle trigonometry.
- Write trigonometric functions in terms of cofunctions.
- Find reference angles and use them to find exact trigonometric function values.
- Find trigonometric function values using a non-graphing scientific calculator.
- Solve applied problems using right triangles.

- Unit Circle
- Convert between degree and radian angle measures.
- Find arc length and area of a sector for circles.
- Draw and use the unit circle to find exact trigonometric function values.
- Find linear and angular speed.

- Graphs of the Trigonometric Functions
- Graph sine and cosine functions.
- Graph vertical and horizontal translations, expansions, and contractions for the sine and cosine functions.
- Graph tangent and cotangent functions.
- Graph secant and cosecant functions.

- Trigonometric Identities
- Verify trigonometric identities using fundamental identities.
- Verify trigonometric identities using sum and difference identities.
- Verify trigonometric identities using double- and half-angle identities.

- Inverse Trigonometric Functions
- Define inverse trigonometric functions for sine, cosine, and tangent.
- Find inverse trigonometric function values for sine, cosine, and tangent.
- Solve applied problems.

- Trigonometric Equations
- Solve trigonometric equations using algebraic and trigonometric methods.
- Solve applied problems.

- Oblique Triangle Trigonometry
- Use the Law of Sines.
- Use the Law of Cosines.
- Solve applied problems.

- Vectors
- Interpret vectors algebraically.
- Perform vector operations.
- Solve applied problems.

### Assessment and Requirements

Assessment of Academic Achievement

- All students are required to complete a comprehensive final examination that assesses the learning of all course objectives. This final examination must be weighted in a manner so that this exam score is worth a minimum of fifteen percent (15%) of the student's final course grade. In selected semesters this final exam may be a common final exam administered to all sections of MATH-112.
- All students will be required to complete at least two (2) proctored on-campus exams. The cumulative value of these exams must be at least forty percent (40%) of a student's final course grade.
- For proctored in-person formal assessments (quizzes, tests, and exams) the only technology students can use is a non-graphing scientific calculator. Quizzes, tests, and exams may have non-calculator parts. Class projects and informal assessments will require students to use a free graphing application to support learning.
- Additional assessment of student achievement may include assignments, quizzes, and exams.
- Application problems must not only be included on chapter exams but also on the final exam.
- All students will be required to complete online homework. This online homework must be weighted in such a manner so that it is worth between six percent (6%) and twelve percent (12%) of the final course grade.

General Course Requirements and Recommendations

- A non-graphing scientific calculator is required for formal assessments.
- Free graphing applications may be used to support learning for informal assessments and class work.
- Access to an online homework management system is required.
- Application problems must be covered in all mathematics courses. Every section in any course outline that includes application problems must be covered.

### Outcomes

General Education Categories

- Mathematics

Institutional Outcomes

- Quantitative Literacy

Satisfies Wellness Requirement

No

### Approval Dates

Effective Term

Fall 2024

Review Semester

Fall 2024