Pre-Calculus+-+Trigonometry


 * Course:** MTH 112/Pre-Calculus B
 * Teacher:** Ameena Amdahl-Mason
 * Articulation:** 5 college credits may be awarded
 * Textbook:** __Algebra and Trigonometry with Modeling and Visualization__, 3rd ed., Gary Rockswold, Pearson/Addison Wesley.

This course is part II of a pre-calculus sequence that provides exploration and application of rational and trigonometric functions and their inverses modeled algebraically, numerically, and graphically; trigonometric identities and equations; vectors; parametric equations; and polar equations. Real world applications are emphasized. Trigonometric understanding is developed using the unit circle. Topics include trigonometric functions and their inverses, graphs of trigonometric functions, equations and identities, applications, an introduction to vectors, polar graphs, complex numbers, and conic sections.
 * Course Description**

This course is intended to accomplish the following: · Present pre-calculus content using the Rule of Four. · The Rule of Four: Each topic should be presented symbolically, graphically, numerically, and verbally. · Introduce students to periodic functions and their properties. · Define sine and cosine functions based on the unit circle. · Define radian measure and describe the relationship between radians and degrees. · Use radian measure to describe the length of an arc. · Introduce students to trigonometric values for particular angles. · Describe and transform sine and cosine graphs. · Define tangent, secant, cosecant, and cotangent functions in terms of sine and cosine functions. · Define the inverse trigonometric functions. · Use inverse trigonometric functions to model applications and solve problems. · Relate unit circle trigonometry to right triangle trigonometry. · Introduce and use the laws of sines and cosines. · Use trigonometric identities to solve equations. · Model applications using trigonometry. · Define polar coordinates. · Describe the relationship between polar and Cartesian coordinates. · Graph functions in polar coordinates. · Introduce complex numbers. · Use polar representations of complex numbers. · Introduce students to vectors, vector arithmetic, and vector algebra. · Use vectors to model applications and solve problems. · Use parametric equations to describe curves. · Define curves implicitly. · Introduce the conic sections. · Use conic sections to model applications and solve problems. · Demonstrate an appropriate use of technology to solve problems. · Use technology to fit functions to data sets.
 * Course Objectives**

Upon completion of this course, the student is expected to be able to accomplish the following: · Define and identify periodic functions. · Define the sine and cosine functions in terms of the unit circle. · Convert between radian measures and degree measures. · Use radians to compute the length of an arc. · Evaluate the sine and cosine functions for particular angles. · Graph the sine and cosine functions. · Transform sine and cosine graphs. · Define and identify the tangent, secant, cosecant, and cotangent functions. · Define and identify the inverse trigonometric functions. · Use inverse trigonometric functions to solve equations. · Use inverse trigonometric functions to model applications and solve problems. · Relate unit circle trigonometry and right triangle trigonometry. · Solve problems using the laws of sines and cosines. · Use trigonometric identities to solve equations. · Use trigonometry to model applications and solve problems. · Convert between Cartesian and polar coordinates. · Graph polar functions. · Define, describe, and compute with complex numbers. · Give polar representations of complex numbers. · Define and describe vectors. · Perform vector arithmetic and vector algebra. · Use vectors to model applications and solve problems. · Describe curves using parametric equations. · Graph implicitly defined functions. · Determine the equations of conic sections. · Graph conic sections. · Use conic sections to model applications and solve problems. · Demonstrate rigorous and analytical thinking by reading, writing, and utilizing the technical and logical language and symbolism necessary to do mathematics and to solve problems effectively and efficiently. · Work effectively as a team member to engage in problem solving. · Use technology effectively to model and solve applications in pre-calculus.
 * Learning Objectives**

· Periodic Functions · Sine and Cosine Functions · Trigonometric Functions · Inverse Trigonometric Functions · Right Triangle Trigonometry · Laws of Sines and Cosines · Trigonometric Identities · Polar Coordinates · Complex Numbers · Vectors · Vector Arithmetic · Parametric Equations · Implicitly-defined functions · Conic Sections
 * Major Topic Outline**


 * Sequence of Assignments**
 * < Chapter ||< Sections Covered ||< Tests ||
 * < 6 ||< 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 ||< Chapter 6 Test ||
 * < 7 ||< 7.1, 7.2, 7.3, 7.4, 7.5 ||< Chapter 7 Test ||
 * < 8 ||< 8.1, 8.2, 8.3, 8.4, 8.5, 8.6 ||< Chapter 8 Test ||
 * < 9/10 ||< 9.1, 9.2, 9.3, 10.1, 10.2, 10.3 ||< Chapter 10 Test ||
 * <  ||< selected topics from Chapter 11, Review ||< Final ||

Students are expected to attend every class. If a student misses a class, it is his or her responsibility to ask for assignments and make up the work. Any missed tests or quizzes must be rescheduled within 24 hours of returning from an absence.
 * Attendance Policy**

Homework = 35 % Tests = 55 % Final = 10 %
 * Grading Rubric**