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# MATH 1062 - College Algebra II with Trigonometry

Credits: 5
Hours/Week: Lecture 5 Lab None
Course Description: This course is the second course of a two-semester sequence for students planning to take MATH 1081 - Single Variable Calculus I . Topics include right triangle trigonometry, trigonometric functions of any real number, graphs of trigonometric functions, trigonometric equations and identities, and inverse trigonometric functions. Course content will also cover systems of non-linear equations and inequalities, sequences and series, parametric equations, polar coordinates, conic sections, and basic vector operations. A graphing calculator is required. Instruction will be provided in the use of the TI-83/TI-84 calculator.
MnTC Goals
4 Mathematics/Logical Reasoning

Prerequisite(s): Placement into MATH 1062 or higher, or MATH 1061  with a grade of C or higher.
Corequisite(s): None
Recommendation: Eligible for college-level Reading and English.

Major Content

1. Sequences and Series
1. Sequences
2. Summation notation and series
3. Arithmetic sequences and series
4. Geometric sequences and series
5. The Binomial Theorem
2. Analytic Geometry and Additional Topics
1. Parabolas
2. Ellipses
3. Hyperbolas
4. Parametric equations
5. Polar coordinates
6. Graphs of polar equations
7. Polar form of a complex number
8. Vector operations including the dot product
3. Trigonometric Functions and Applications
2. Trigonometric functions: the unit circle
3. Right triangle trigonometry
4. Trigonometric functions of any angle
5. Graphs of trigonometric functions
6. Inverse trigonometric functions
7. Laws of Sines and Cosines
8. Applications and models
4. Systems of Equations and Inequalities
1. Partial fractions
2. Systems of nonlinear equations and inequalities
5. Analytic Trigonometry
1. Fundamental identities
2. Verifying identities
3. Trigonometric equations
4. Sum and Difference formulas
5. Multiple-angle and half-angle formulas

Learning Outcomes
At the end of this course students will be able to:

1. define trigonometric functions in terms of right triangles and the rectangular coordinate system.
2. evaluate trigonometric functions of any angle with technology.
3. evaluate trigonometric functions of angles whose reference angle is a special angle by hand.
4. simplify trigonometric expressions by applying trigonometric definitions and trigonometric identities.
5. convert between degree measure and radian measure.
6. solve problems involving similar triangles.
7. demonstrate critical and logical reasoning when solving problems.
8. determine the period, amplitude, and phase shift of sine and cosine functions symbolically.
9. find the area of a triangle using trigonometric formulas.
10. graph trigonometric functions and conic sections analytically and by using graphing technology.
11. solve non-linear systems of equations and inequalities symbolically and graphically.
12. solve triangles symbolically by using right triangle trigonometry, the Law of Sines, and the Law of Cosines.
13. solve trigonometric equations using algebraic, graphical, and numerical methods.
14. verify trigonometric identities using the techniques of analytic trigonometry.
15. analyze sequences and series.
16. convert among polar, parametric, and rectangular equations.
17. graph polar, parametric, and rectangular functions.
18. model and solve applied problems using the techniques of trigonometry, and analytic geometry.
19. perform basic vector operations.
20. communicate clearly a problem’s solution and its explanation for the intended audience in terms of the problem posed.
21. determine partial fraction decomposition.

Competency 1 (1-6)
04. 01. Illustrate historical and contemporary applications of mathematical/logical systems.

04. 02. Clearly express mathematical/logical ideas in writing.

04. 03. Explain what constitutes a valid mathematical/logical argument(proof).

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