Download MAT 181 Plane Trigonometry

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Course Package
MAT 181
PLANE TRIGONOMETRY
PRESENTED AND APPROVED: SEPTEMBER 7, 2012
EFFECTIVE: FALL 2012-13
MCC Form EDU 0007 (rev. 10/07/11)
INSTRUCTION
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Prefix & Number MAT 181
Purpose of this submission:
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Course Title: Plane Trigonometry
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Course Description
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Competencies
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Does this course require additional fees?
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Yes If so, please explain.
Is there a similar course in the course bank?
No
Yes (Please identify)
Articulation: Is this course or an equivalent offered at other two and four-year universities in Arizona?
No
Yes (Identify the college, subject, prefix, number and title: U of A, MATH 111, ASU/NAU –
MAT DEPT ELECTIVE
Is this course identified as a Writing Across the Curriculum course?
No
Yes
Course Textbook, Materials and Equipment
Textbook(s)
Current
edition
Title
Author(s)
Publisher
Trigonometry, 9th ed.
Lial, Hornsby, Schneider
Pearson
Title
Author(s)
Publisher
Software/
Equipment
MyMathLab Access/Review of Algebra/Student Solutions, Manual/Digital
Video Tutor bundled with text: ISBN: 0321294718 (DE)
A graphing calculator is required. A TI83/84 calculator is highly recommended and keystrokes will be
modeled by the instructor using these calculators.
Course Assessments
Description of Possible Course Assessments (Essays, multiple choice,
etc.)
Exams standardized for this course? No; each instructor makes up
his/her own exams.
Midterm
Final
Other (Please specify):
Where can faculty members locate or access the required standardized
exams for this course?
MCC Form EDU 0007 (rev. 10/07/11)
Multiple choice less appropriate; Short answer,
open answer problems more appropriate.
Assessment questions should be similar in
nature to textbook homework problems.
Are exams required by the department?
No
Yes
If Yes, please specify:
Clark Brown, Neal Campus, Kingman
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Course Package
Student Outcomes: Identify the general education goals for student
learning that is a component of this course.
Check all that apply:
Method of Assessment
1. Communicate effectively.
a.
b.
Read and comprehend at a college level.
Write effectively in a college setting.
2. Demonstrate effective quantitative reasoning and problem
solving skills.
3. Demonstrate effective qualitative reasoning skills.
4. Apply effective methods of inquiry.
a. Generate research paper by gathering information
from varied sources, analyzing data and organizing
information into a coherent structure.
b. Employ the scientific method.
5. Demonstrate sensitivity to diversity
a. Experience the creative products of humanity.
b. Describe alternate historical, cultural, global
perspectives.
Office of Instruction Use only:
CIP Code:
ONET Code:
Minimum Qualifications:
MCC Form EDU 0007 (rev. 10/07/11)
Midterm and Final Exams
INSTRUCTION
Course Package
COURSE INFORMATION
Initiator: Clark Brown
Date of proposal to Curriculum Sub-Committee: September 2012
Effective Semester/Year
Fall 2012
Competencies and Course Description will be effective Fall 2013.
Prefix & Number: MAT 181
Full Title: (100 character limit)
Plane Trigonometry
Short Title: (30 character limit)
Trigonometry
Catalog Course Description: A study of the trigonometric functions and their graphs and inverses,
trigonometric identities, and the applications of these functions to right and oblique triangles, vectors,
complex numbers, and polar and parametric equations.
SUN Course Number:
Credit Hours: 3
Lecture Hours: 3
Lab Hours: 0
Prerequisite(s) Grade of “C” or better in Math 151, or appropriate score on the college’s math
placement test
Co-requisite(s) None
Intended Course Goals
By the end of the semester, students will be able to:
1. Define the trigonometric functions in terms of the terminal side of an angle, right triangles, and the
unit circle.
2. Solve applied problems using the trigonometric relationships.
3. Describe angles using both degree and radian measure and identify the exact trigonometric
function values for special angles in any quadrant.
4. Graph transformations of each of the basic trigonometric functions
5. Transform trigonometric expressions using identities and solve trigonometric equations using
inverse trigonometric functions.
6. Apply the concepts of trigonometry to solve problems involving oblique triangles, vectors, complex
numbers, and polar and parametric equations.
MCC Form EDU 0007 (rev. 10/07/11)
INSTRUCTION
Course Package
Course Competencies and Objectives
By the end of the semester, students will be able to:
Competency 1 Interpret the trigonometric functions in terms of a point in the Cartesian plane on the terminal side of an
angle.
Objective 1.1 Convert between decimal degree and degree-minute-second (DMS) format for angle measure.
Objective 1.2 Perform angle operations using decimal degree and DMS format.
Objective 1.3 Solve applied problems using the basic relationships of similar triangles, vertical angles, and the angle
sum of a triangle.
Objective 1.4 Define the trigonometric functions as ratios of x, y, and r, where (x,y) is a point on the terminal position of
an angle and r is the distance of (x,y) from the origin.
Objective 1.5 Apply the reciprocal, Pythagorean, and quotient identities
Objective 1.6 Give the sign of each trigonometric function in each quadrant of the Cartesian plane.
Competency 2 Interpret the trigonometric functions in terms of right triangles.
Objective 2.1 Define the trigonometric functions in terms of the acute angles of a right triangle.
Objective 2.2 Use reference angles to define the trigonometric functions for non-acute angles.
Objective 2.3 Apply the co-function identities.
Objective 2.4 Find trigonometric function values using a calculator.
Objective 2.5 Solve right triangle problems, including angle of elevation/depression and bearing problems, using the
trigonometric relationships.
Competency 3 Interpret the trigonometric functions in terms of the unit circle.
Objective 3.1 Define radian measure.
Objective 3.2 Convert between radians and degrees.
Objective 3.3 Find trigonometric functions values for angles given in radian measure.
Objective 3.4 Apply radian measure to find arc length and area of a sector of a circle.
Objective 3.5 Define the trigonometric functions in terms of the unit circle.
Objective 3.6 Explain how the domain of the trigonometric functions is extended from angles to the real numbers.
Objective 3.7 Apply the relationship between linear and angular speed to solve problems relating to these concepts.
Competency 4 Graph circular functions by translating graphs of the basic functions.
Objective 4.1 Identify the basic graphs of the six trigonometric functions.
Objective 4.2 Identify the key features of a periodic function from its equation, including amplitude, period, phase shift
and vertical translation.
Objective 4.3 Graph trigonometric functions by using the key features and transformations of the basic graphs of the
six trigonometric functions.
Objective 4.4 Create equations to model periodic phenomena and simple harmonic motion using trigonometric
expressions.
Competency 5 Apply trigonometric identities to transform trigonometric expressions.
Objective 5.1 Apply the reciprocal, quotient, co-function, Pythagorean and Negative-Angle Identities.
Objective 5.2 Apply the sum, difference, and double- and half-angle identities for sine, cosine and tangent.
Objective 5.3 Apply the product-to-sum and sum-to-product identities for sine and cosine.
Objective 5.4 Verify trigonometric identities using algebraic and graphical techniques.
Competency 6 Apply the inverse trigonometric functions to solve algebraic equations involving trigonometric functions.
Objective 6.1 Derive the inverse trigonometric functions by restricting the domain of the trigonometric functions
appropriately.
Objective 6.2 Describe the basic graphs and domain and range of the inverse trigonometric functions.
Objective 6.3 Solve trigonometric equations using identities, factoring, and linear and quadratic methods.
Objective 6.4 Solve trigonometric equations with half-angles and multiple angles.
Objective 6.5 Solve equations involving inverse trigonometric functions.
Competency 7 Apply trigonometry to oblique triangles and vectors.
Objective 7.1 Solve SAA and ASA triangles using the law of sines.
Objective 7.2 Solve SSA triangles, including the ambiguous case, using the law of sines.
Objective 7.3 Solve SAS and SSS triangles using the law of cosines.
MCC Form EDU 0007 (rev. 10/07/11)
INSTRUCTION
Course Package
Objective 7.4 Find the area of an oblique triangle.
Objective 7.5 Perform vector operations both graphically and algebraically.
Objective 7.6 Find the angle between two vectors using the dot product.
Objective 7.7 Solve incline and navigation applications using vectors.
Competency 8 Apply trigonometry to the trigonometric form of complex numbers and polar and parametric equations.
Objective 8.1 Convert between the trigonometric (polar) form of a complex number and its rectangular form.
Objective 8.2 Multiply complex numbers in polar form using the product theorem.
Objective 8.3 Divide complex numbers in polar form using the quotient theorem.
Objective 8.4 Find powers and roots of complex numbers using DeMoivre’s Theorem.
Objective 8.5 Contrast the polar coordinate system with the rectangular system.
Objective 8.6 Graph polar equations.
Objective 8.7 Convert between polar and rectangular equations.
Objective 8.8 Describe a plane curve using parametric equations.
Objective 8.9 Graph plane curves defined parametrically.
Objective 8.10 Find the rectangular equivalent to a parametric graph.
MCC Form EDU 0007 (rev. 10/07/11)