# MATH 118

**Review.*** Prerequisite Material from MATH 117* [1.5 Weeks]

Quick review of algebra, lines, circles, quadratic expressions, and functions, followed by a more comprehensive review of the definitions and properties of exponential functions and logarithms. Exponential growth modeling can be covered lightly.

**Chapter 8.** *Sequences, Series, and Limits* [2 Weeks]

8.1 – Sequences: definition of sequence, arithmetic/geometric sequences, recursively defined sequences.

8.2 – Series: sums of sequences, definition of series, arithmetic/geometric series. Emphasize: summation notation. Binomial theorem is optional.

8.3 – Limits: introduction to limits, infinite series, decimals as series, special series.

**Chapter 9.** *Trigonometric Functions* [3 Weeks]

9.1 – The unit circle: equation of unit circle, angles, negative angles, angles greater than 360 degrees, arc length, special points on unit circle.

9.2 – Radians: motivation of radians, radius corresponding to an angle, arc length revisited, area of slices, special points on unit circle revisited.

9.3 – Cosine and sine: definition of cosine and sine, signs of cosine and sine, pythagorean identity, graphs of cosine and sine.

9.4 – More trigonometric functions: tangent, sign of tangent, connections between cosine, sine, and tangent, graph of tangent, definitions of cotangent, secant, cosecant.

9.5 – Trigonometry in right triangles: definition of trigonometric functions via right triangles, two sides of a right triangle, one side and one angle of a right triangle

9.6 – Trigonometric identities: relationship between cosine, sine, tangent, identities for negative angles, identities involving pi/2, identities involving multiples of pi

**Chapter 10.** *Trigonometric Algebra and Geometry* [3 Weeks]

10.1 – Inverse trigonometric functions: arccosine, arcsine, and arctangent functions.

10.2 (Optional) – Inverse trigonometric identities, graphical and algebraic approach to evaluation at –*t*

10.3 – Using trigonometry to compute area: area of triangle/parallelogram via trigonometry, ambiguous angles, areas of polygons, trigonometric approximations.

10.4 – Law of Sines and Law of Cosines: statement and uses of laws of sines/cosines, when to use which law.

10.5 – Double-Angle and Half-Angle Formulas: sine/cosine double-angle and half-angle formulas. The corresponding formulas for tangent are optional.

10.6 – Addition and subtraction formulas: sine/cosine/ sum and difference formulas. The corresponding formulas for tangent are optional.

**Chapter 11.** *Applications of Trigonometry* [2.5 Weeks]*Suggestion:* If time is short, 11.1 is optional. Focus on 11.2, 11.3, and 11.5.*Suggestion:* Quickly review Chapter 3, Section 2 before covering 11.2

11.1 (Optional) – Parametric curves: curves in the plane, inverse functions as parametric curves, shifts/flips of parametric curves. Stretches of parametric curves is optional.

11.2 – Transformations of trigonometric functions: amplitude, period, phase shift, modeling periodic phenomena, modeling with data.

11.3 Polar Coordinates: Definition of polar coordinates, conversion between polar/rectangular coordinates, graphs of circles and rays. Other polar graphs are optional.

11.4 (Optional) – Algebraic and geometric introduction to vectors, addition and subtraction, scalar multiplication, dot product.

11.5 – The complex plane: complex numbers as points in the plane, geometric interpretation of multiplication/division of complex numbers, De Moivre's theorem, finding complex roots.

There is one required book for this course:

Axler, Sheldon. *Precalculus: A Prelude to Calculus, 2nd Edition* Paperback w/ Wileyplus ISBN: 978-1-118-55625-2. Hoboken, NJ: Wiley, 2012.

Many instructors do require WileyPLUS. If your section is using WileyPLUS, it is important that you buy a bundle that includes a WileyPLUS access code since you will need it in order to submit homework. A WileyPLUS access code includes an online electronic version of the textbook. You can obtain an access code in one of three ways:

- Buy a new copy of the text bundled with WileyPLUS access code from the bookstore.
- Buy a
*Precalculus: A Prelude to Calculus 2E*access code directly from the publisher’s website. - Buy a Precalculus: A Prelude to Calculus 2E WileyPLUS access code directly from the bookstore.

**Note on WileyPLUS access:** If you purchased a MATH 118 access code over the past year, you will not need to purchase another one. Your access code is valid for one year.

**Note on Textbook:** Students who were enrolled in MATH 117 or MATH 118 in Spring 2014 will not have to purchase the new edition of the textbook. (See course instructor for details.)

If you go for option (2) or (3) above, then you will only have access to the book electronically through WileyPLUS. Whether you have purchased an access code or not, all students have immediate and free access to register for our class WileyPLUS page. **Free trial access expires two weeks after the semester starts.**

### Center for Tutoring and Academic Excellence

The Center for Tutoring & Academic Excellence offers free collaborative learning opportunities that include small group tutoring and tutor-led study halls to Loyola students. To learn more or request tutoring services, visit the Center for Tutoring & Academic Excellence online at http://www.luc.edu/tutoring.

### Loyola Math Club Tutoring

The Loyola Math Club offers free tutoring to students in Math 118 (and other courses). Further details regarding the important information of where and when will be posted once announced.

WileyPLUS is an online, interactive environment for teaching and learning. As part of the required text for MATH 118, you are asked to purchase an access code for WileyPLUS. This access code is active for up to one year. Thus, if you used WileyPLUS in MATH 117 in Fall 2012, your access code from last semester will allow you to enroll in your MATH 118 section this semester at no extra cost. Many sections of MATH 118 will use WileyPLUS as a required homework component of the final course grade.

Follow the steps below to register for your section in WileyPLUS:

- Go to the WileyPLUS homepage.
- In the Students section of the homepage, click on the
**Get started**button. - Enter
**LOYOLA UNIV - CHICAGO**as the school name and click**Find**. - Click the plus sign next to
**PRECALCULUS/MATH 118**to expand the section list. - Click on your section.
- Create a WileyPLUS account or log in using an existing account.
- If you have purchased a hard copy of the text with the access code, enter your code to register for the course. Otherwise you can purchase a code (for $55.00).

**Note: All students may register for WileyPLUS immediately, even if you have not received your copy from the bookstore at the start of the semester. If you have not received an access code by January 28, you will no longer have access to WileyPLUS.**

Mathematica is a powerful computing environment that is designed for use in engineering, mathematics, finance, physics, chemistry, biology, and a wide range of other fields. Loyola students and faculty can download and install the latest copy of Mathematica for free. You must be logged on to Loyola VPN, and then visit the following ITS webpage, https://digitalmedia.luc.edu/News/NewsItem/View/4/mathematica-version-9-downloads-available.

## Other Useful Loyola Sites

- Sakai (Online Course Materials)
- Tutoring Center
- Get
*Mathematica*for***free***through myITS - WebWork