MAT 156 - Algebra and Trigonometry for Calculus
Graphs of rational functions, asymptotes, exponential and logarithmic equations, conic sections, matrix arithmetic and matrix solutions to systems of equations, determinants, trigonometric identities and equations, Law of Sines, Law of Cosines, vectors, polar graphs, parametric graphs, polar form of complex numbers, powers and roots of complex numbers, limits of functions using tables.
Prerequisite: MAT 136 College Algebra and Trigonometry or equivalent
4 Class Hours
Learning Outcomes of the Course:
Perform skills in three categories: Algebra, Geometry, and Trigonometry.
Note: Throughout the course the students are expected to solve applied problems related to the topics of the course.
Upon successful completion of this course the student will be able to:
Algebra, Geometry, Trigonometry Objectives:
1. Determine the horizontal, vertical, and oblique asymptotes of a rational function.
2. Solve rational, polynomial, exponential, logarithmic, trigonometric equations analytically.
3. Solve rational and polynomial inequalities analytically.
4. Graph Inx, ex, logax and ax.
5. Name the equation of a transformed basic function/relation by viewing its graph.
6. Construct a graph of a rational function from its intercepts and asymptotes.
7. Solve systems of linear equations using substitution, elimination and row operations on matrices.
8. Perform the partial fraction decomposition of a rational expression.
9. Solve systems of linear inequalities.
10. Find the determinant of 2 by 2 and 3 by 3 matrices.
11. Add, subtract, multiply matrices.
12. Verify trigonometric identities involving the reciprocal identities, quotient identities, Pythagorean identities, angle sum identities, double angle identities, and half angle identities.
13. Solve problems involving inverse trigonometric functions
14. Graph y=sin-1x, y=cos-1, y=tan-1, y=sec-1x on a suitable domain.
15. Apply the Law of Sines to solve application problems.
16. Explain and solve the ambiguous case for the Law of Sines.
17. Apply the Law of Cosines to solve application problems.
18. Define a vector.
19. Perform vector arithmetic, including magnitude.
20. Use component vectors to solve application problems.
21. Convert between trigonometric (polar) and rectangular forms of complex numbers.
22. Find the real and complex zeroes of a polynomial function.
23. Compute powers and roots of complex numbers.
24. Solve problems involving conic section formulas for a circle, parabola, ellipse, and hyperbola.
25. Graph conic sections.
26. Graph basic parametric equations and basic polar equations.
This course prepares students to meet the Mathematics General Education requirement.
In the context of the course objectives listed above, upon successful completion of this course the student will be able 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. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
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