PREREQUISITE: MAT104 - College Algebra with Trigonometry I, equivalent, or placement; placement into ENG101 and college-level reading, or completion of ENG101S and RDG095.

COREQUISITE: None 

This course uses Open Educational Resources (OER). These are freely accessible educational materials that replace traditional textbooks. A $10 OER fee replaces the cost of a textbook for this course.

REQUIRED MATERIALS:

• A graphing calculator (the TI-83, TI-83 Plus, or TI-84 Plus)

COURSE OBJECTIVES:

As the result of instructional activities, students will be able to: 

1. Graph basic power functions and their transformations.
2. Identify even and odd functions based on their symmetries.
3. Use the leading coefficient to determine the end behavior of graphs of polynomial functions.
4. Perform long and synthetic division.
5. Use the Remainder and Factor Theorems.
6. Write the equation of a polynomial function given its zeros.
7. Apply the Rational Zero Test to find all the possible rational zeros of a polynomial function.
8. Perform basic operations with complex numbers.
9. Find all zeros of polynomial functions, including complex zeros.
10. Determine the domain and intercepts of rational functions algebraically and graphically.
11. Determine the vertical, horizontal, and oblique (slant) asymptotes of rational functions algebraically. 
12. Graph rational functions by hand.
13. Solve polynomial and rational inequalities algebraically and graphically.
14. Convert between radian and degree measure.
15. Use right triangle trigonometry to solve applications.
16. Find the six trigonometric functions of any angle.
17. Determine the amplitude, period, domain and range of sine and cosine functions. 
18. Graph sine and cosine curves by hand.
19. Determine the domain, range, and asymptotes of the tangent function.
20. Use the graphing calculator to find a sinusoidal regression equation to model real-life data.
21. Use the inverse trigonometric functions to determine an angle.
22. Use trigonometric identities to simplify trigonometric expressions.
23. Prove basic trigonometric identities.
24. Use the sum and difference formulas to find exact values.
25. Use the double and half-angle formulas to find exact values.
26. Solve trigonometric equations involving a single trigonometric function, algebraically and graphically.
27. Solve trigonometric equations using identities. 
28. Solve oblique triangles using the law of sines (SAA, ASA, SSA).
29. Solve oblique triangles using the law of cosines (SAS, SSS).
30. Solve applications of oblique triangles. 
31. Plot points using polar coordinates.
32. Convert between polar coordinates and rectangular coordinates.
33. Use the midpoint and distance formulas.
34. Find the center and radius of a circle and graph it. 
35. Find the vertex, focus, and directrix of a parabola and graph it.
36. Find the center, major axis, foci, and vertices of an ellipse and graph it. 
37. Find the center, transverse axis, vertices, and foci of a hyperbola and graph it.
38. Identify a conic given its equation 

 If time allows: 

1. Solve a system of linear equations in two variables by substitution or elimination.
2. Identify a system as consistent or inconsistent and its equations as dependent or independent. 
3. Solve systems of three equations in three variables algebraically. 
4. Solve systems of linear equations using matrices. 
5. Find the sum and difference of two matrices.
6. Find scalar multiples of a matrix.
7. Find the product of two matrices.
8. Find the inverse of a matrix.
9. Solve systems of equations using an inverse matrix.
10. Solve systems of nonlinear equations algebraically and graphically

SUNY GENERAL EDUCATION LEARNING OUTCOMES:

Students will demonstrate the ability to: 

1. interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics;
2. represent mathematical information symbolically, visually, numerically and verbally;
3. use arithmetical, algebraic, geometric and statistical methods to solve problems;
4. estimate and check mathematical results for reasonableness; and
5. recognize the limits of mathematical and statistical methods.

GENERAL TOPICS OUTLINE:

1. Polynomial and Rational Functions- including graphs, zeros of polynomial functions, fundamental theorem of algebra, complex zeros, advanced graphs of rational functions
2. Trigonometric Functions- including radian and degree measure, right triangle trigonometry, the unit circle, inverse trig functions
3. Graphs of Trigonometric Functions- including graphs of trigonometric functions, transformations, sinusoidal regression
4. Analytic Trigonometry- including fundamental identities, solving trigonometric equations
5. Applications of Trigonometry- including laws of sines and cosines, polar coordinates
6. Analytic Geometry- including circles, ellipses, parabolas, hyperbolas
7. Systems of Equations and Matrices- including solving systems of linear equations using substitution and elimination; systems of nonlinear equations
8. Matrices- including matrix operations; inverse matrices, matrix equations 

Feel free to contact a member of the Math Department or the Math Department Chair.