MAT182 - Trigonometry with Algebra Review
Course Information
(effective Fall 2015)
Textbook Information
Title:
Precalculus A Right Triangle Approach, 5th edition
Author:
Beecher/Penna/Bittinger
Publisher: Pearson
ISBN: 978-0-321-98955-2
Catalog Description: A comprehensive coverage of trigonometry and selected topics
from college algebra, including measurements of angles, trigonometric functions and
inverse trigonometric functions, trigonometric equations and identities, graphing of
trigonometric functions, solutions of triangles, applications, complex numbers, polar
coordinates, DeMoivre's theorem, logarithms, exponential functions, partial fraction
decomposition, conic sections, sequences and series.
Sections to Cover
Chapter or
Supplement
Chp. 5
Section
5.1
5.2
5.3
5.4
5.5
5.6
Chp. 6
Chp. 7
6.1
6.2
6.3
6.4
6.5
6.6
7.1
7.2
7.3
7.4
Topic
Inverse Functions
Exponential Functions and Graphs
Logarithmic Functions and Graphs
Properties of Logarithmic Functions
Solving Exponential and Logarithmic Equations
Applications and Models: Growth and Decay; Compound
Interest
Trigonometric Functions of Acute Angles
Applications of Right Triangles
Trigonometric Functions of Any Angle
Radians, Arc Length, and Angular Speed
Circular Functions: Graphs and Properties
Graphs of Transformed Sine and Cosine Functions
Identities: Pythagorean and Sum and Difference
Identities: Cofunctions, Double-Angle, and Half-Angle
Proving Trigonometric Identities
Inverses of the Trigonometric Functions
Notes
Chp. 8
Chp. 9
Chp. 10
Chp. 11
7.5
8.1
8.2
8.3
8.4
8.5
8.6
9.1
9.2
9.8
10.1
10.2
10.3
10.5
10.6
10.7
11.1
11.2
11.3
Solving Trigonometric Equations
The Law of Sines
The Law of Cosines
Complex Numbers: Trigonometric Notation
Polar Coordinates and Graphs
Vectors and Applications
Vector Operations
Systems of Equations in Two Variables
Systems of Equations in Three Variables
Partial Fractions
The Parabola
The Circle and the Ellipse
The Hyperbola
Rotation of Axes
Polar Equations of Conics
Parametric Equations
Sequences and Series
Arithmetic Sequences and Series
Geometric Sequences and Series
Optional
MAT 182
Learning Outcomes and Standards
Learning Outcome
1. Apply trigonometric concepts to solve right and
non-right triangle problems.
2. Solve problems involving circles and angles.
3. Identify and sketch the graphs of trigonometric
functions in rectangular, polar and parametric forms.
4. Solve trigonometric equations using trigonometric
identities and inverse functions.
5. Apply concepts of trigonometry to solve problems
involving vectors.
6. Simplify complex numbers in trigonometric form.
7. Recognize the equations of conic sections and
sketch their graphs.
8. Decompose a rational expression into a sum of
partial fractions.
9. Solve and sketch logarithmic and exponential
equations.
Standard(s)
1a. Define the trigonometric functions as a ratio of two
sides of a right triangle.
1b. Model an application problem with a right triangle
to find the missing quantity of the triangle.
1c. Apply the law of sines and law of cosines to find
the missing quantity of a non-right triangle.
2a. Convert angle measures from degrees to radians
and vice versa.
2b. Determine the arc length and central angle of a
specified portion of a circle.
2c. Calculate the angular and linear speed of an object
moving along a circular path.
3a. Determine the period, amplitude, and appropriate
transformational shifts of a trigonometric equation,
and use the information to graph.
3b. Convert from rectangular to polar equation and
vice versa.
3c. Formulate parametric equations for curves defined
by rectangular equations and vice versa.
3c. Graph plane curves defined by parametric and
polar equations.
4a. Apply trigonometric identities to find the
trigonometric value of an angle.
4b. Prove the validity of a trigonometric statement by
applying the appropriate trigonometric identities.
4c. Solve a trigonometric equation by applying the
properties of equality and trigonometric identities.
5a. Express a vector in component form.
5b. Find the magnitude and direction of a given vector.
5c. Apply the properties of vectors to solve application
problems involving forces and equilibrium.
6a. Convert a complex number to polar form.
6b. Apply the De Moivre’s Theorem to find the nth
roots of a complex number.
7a. Given an equation classify the conic as circle,
parabola, ellipse, or parabola.
7b. Given any characteristic of a conic, write the
equation in standard from.
7c. Sketch the graph of a conic given an equation or
key characteristics.
8. Decompose a rational expression where the
denominator is a product of linear and/or quadratic
factors.
9a. Sketch the graphs of polynomial, exponential and
logarithmic functions using the techniques of
transformation.
9b. Apply the properties of exponents and logarithms
to solve problems involving compound interest and
exponential growth and decay.
10. Distinguish the difference between arithmetic and
geometric sequences.
11. Evaluate the sum of finite and infinite series.
12. Use technology to assist in solving problems.
10a. Find the first term and common difference of an
arithmetic sequence.
10b. Find the first term and common ratio of a
geometric sequence.
10c. Establish an nth term formula for a geometric or
an arithmetic sequence.
11a. Evaluate the sum of an arithmetic series.
11b. Evaluate the sum of a finite and infinite
geometric series.
11c. Evaluate the sum of a series written in summation
notation form.
12. Use calculators (scientific and graphing) and
available computer software to model, investigate,
solve, and justify solutions to given problems.