# MATH 144 Trigonometry*

### Credits

### Prerequisite

MATH 143## MATH 144Trigonometry*

Please note: This is not a course syllabus. A course syllabus is unique to a particular section of a course by instructor. This curriculum guide provides general information about a course.

## I. General Information

### Department

Mathematics & Engineering

## II. Course Specification

### Course Type

### Credit Hours Narrative

### Prerequisite Narrative

### Grading Method

### Repeatable

## III. Catalog Course Description

This course covers right triangle and circular function approaches to trigonometry, graphs of trig functions, trig identities, conditional equations, right and non-right triangle applications of trigonometry, inverse trig functions, trigonometry of complex numbers including DeMoivre's Theorem, polar coordinates and equations, parametric equations. Students desiring both college algebra and trigonometry should take MATH 147. Credit hours are not granted in both MATH 144 and MATH 147.

## IV. Student Learning Outcomes

Upon completion of this course, a student will be able to:

- Demonstrate applying the trigonometric concepts to skill-based problems from the course content listed in section V.
- Evaluate and graph, and understand individual characteristics of the trigonometric functions
- Verify and apply trigonometric identities to skill-based problems
- Apply the appropriate trigonometric tools to help analyze real world questions and mathematically structure the models of the questions
- Use appropriate trigonometric tools to help analyze real world questions and mathematically structure the models of the questions.

## V. Topical Outline (Course Content)

Angles (standard position, positive angle, negative angle, degree measure in degrees-minutes-seconds as well as decimal degrees, radian measure, coterminal angles, reference angles, supplementary, complementary) Trig functions in right triangles (trig function definitions using opposite side, adjacent side and hypotenuse of right triangle; exact trig values of 30(-60(-90( and 45(-45(-90( triangles; use calculator to evaluate trig function values in degrees and radians; solve right triangles including application problems) Trig functions of any angle (use the x-y-r definitions to find trig function values, signs of the trig functions within each quadrant, find and use reference angles) Trig functions of real numbers (use the unit circle to find trig function values, properties of the trig functions (domain, range, symmetries, period) Basic trig identities (Reciprocal, Quotient or Ratio, Pythagorean, rearrange basic identities, simplify trig expressions) Graph the trig functions (period, amplitude, graph sin, cos, tan, cot, csc and sec functions without the use of a graphing calculator and using a graphing calculator, transformations of the basic trig graphs (horizontal and vertical shifts, vertical stretch/shrink, change of period, graph using addition of ordinates, given the graph of a trig function write the equation) Inverse trig functions (restrictions on the domain and range, how graph of inverse is related to trig function graph, find exact values using triangles, evaluate composition of a trig function and an inverse trig function, evaluate inverse trig functions using a calculator) Verify trig identities (include techniques of changing all to sin and cos, factoring, multiplying by a conjugate, etc., use graphs to decide if a given equation is an identity, then prove algebraically) Use trig identities (Sum and Difference Identities for sin, cos, tan, Cofunction Identities, Double-Angle Identities, Half-Angle Identities, Product to Sum Identities, Sum to Product Identities) Solve trig equations Applications of trig (Linear velocity, angular velocity, arc length, area of a sector, Law of Sines, Law of Cosines, area of a triangle, trigonometric form of complex numbers (compute absolute value, product, quotient), DeMoivre’s Theorem) Parametric equations (eliminate the parameter, graph) Polar coordinates and equations (convert to and from rectangular form, graph)