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Math 1060 Trigonometry Content (2 Semester Credits)
This section covers the content instructors must cover to best prepare their students for successful completion of Math 1060. The basic content may change in the future. However, the official syllabus will be published on the Department of Mathematics and Statistics web site (http://www.math.usu.edu). If the web site is not available, the official syllabus can be obtained by contacting the Department of Mathematics and Statistics at USU.
Current Textbook Information
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ISBN-13: 9780618854639 |
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ISBN-10: 0618854630 |
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Title: Precalculus |
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Subtitle: A Graphing Approach |
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Edition: 5/e |
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Author(s): Ron Larson, Robert P. Hostetler, Bruce H. Edwards, |
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Format: Hardcover |
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Copyright: 2008 |
The publisher web page for the textbook is the following:
Course Content
The following is a summary of the content that must be covered in Math 1060 Trigonometry.
Trigonometric Functions
- Angles and Measuring Angles: basic definitions of angle standard position, positive and negative angles, degree and radian measure, complementary and supplementary angles.
- Right Triangle Trigonometry: definitions of trigonometric functions based on a right triangle using hypotenuse, adjacent side, and opposite side, evaluation of trigonometric functions at special angles, basic trigonometric identities and simplification of trigonometric expressions using the definitions of the trigonometric functions.
- Trigonometric Functions: trigonometric functions evaluated at any angle, reference angles, acute and nonacute angles, trigonometric functions and real numbers, periodic functions and relationship to trigonometric functions, even and odd trigonometric functions.
- Graphs of Sine and Cosine Functions: graphs of sine and cosine functions, amplitude, period, wavelength, translation, stretching and contracting.
- Graphs of General Trigonometric Functions: graphs of general expressions involving trigonometric functions.
- Inverse Trigonometric Functions: definitions of inverse trigonometric functions, restriction of domains and ranges of the inverse trigonometric functions, composition of trigonometric functions.
- Applications of Trigonometric Functions: periodic applications modeled by trigonometric functions, spring mass systems, force balance systems, and so on.
Analytic Trigonometry
- Fundamental Identities: the Pythagorean theorem in trigonometric functions, cofunction identities, even and odd function relationships, combining identities to evaluate trigonometric expressions
- Verifying Trigonometric Identities: algebraic and graphical verification of trigonometric identities.
- Solving Trigonometric Equations: solving equations involving trigonometric functions, factoring, collecting like terms, using trigonometric identities to reduce angles.
- Sum and Difference Formulas: sum and difference identities for trigonometric functions.
- Multiple –Angle and Produce to Sum Formulas: identities for reduction to one angle in trigonometric functions, double and half angle formula, sum to product formulas.
More Trigonometric Identities
- Law of Sines: definition and application of the law of sines to trigonometric problems.
- Law of Cosines: definition and application of the law of cosines to trigonometric problems
- Vectors in the Plane: definitions of vectors in terms of length and angles, using trigonometric functions for solving vector problems.
- Vectors and the Dot Products: angles, dot products, unit vectors, projections, computing the angle between two vectors, relationship trigonometric functions.
