7/27/2019 syllabus_OM013

1/2

ONLINE HIGH SCHOOL

OM013:HonorsPrecalculuswithTrigonometry

CourseDescription

Honors Precalculus with Trigonometry covers the background in mathematical analysis, linear algebra, and

trigonometry needed for success in Advanced Plac ement calculus. Building on a solid b ackground in algebra and

geometry, students deepen their understanding of equations and inequalities involving linear, quadratic, and higher

degree polynomials. Important theorems about polynomials such as the Factor Theorem and the Rational Roots

Theorem are studied. Students also investigate exponential and logarithmic functions, and they learn to use these

functions to model real-world situations. Students learn basic right-angle trigonometry, master the trigonometric

functions as defined on the real number line, and apply general principles to graph and understand the qualitative

properties of such functions. The definitions and graphs of the inverse trigonometric functions are also covered. Students

master the full range of trigonometric identities and use this knowledge to evaluate and prove additional identities.

Following a treatment of equations involving trigonometric and inverse trigonometric functions, students learn the

important Law of Sines and Law of Cosines.

The trigonometry portion of the course finishes with a treatment of v ectors, the trigonometric form for complex numbers,

and DeMoivre's Theorem. Students then learn the Gauss-Jordan method for solving linear equations and study the

properties of matrix algebra. Following this, students learn special techniques used in solving nonlinear equations and

inequalities. The course ends with an investigation of ad ditional topics incl uding mathematical induction, the Binomial

Theorem, arithmetic series, and geometric series.

RequiredText

Precalculus

Lial, Hornsby, Schnieder, and Daniels

CourseTopics

Honors Precalculus with Trigonometry requires that students master the following specific topics:

Algebraic ExpressionsThe Real Number System, Absolute Value, Polynomials, Rational Expressions, Radicals, Complex Numbers

Equations and InequalitiesLinear Equations, Absolute Value Equations, Quadratic Equations, Inequalities

Relations and FunctionsThe Cartesian Plane, Functions, Graphing Techniques, The Algebra of Functions, Inverse Functions, Variation

Polynomial and Rational FunctionsLinear Functions, Quadratic Functions, Polynomial Functions of Higher Degree, Polynomial Long Division,

Complex Zeros of Polynomials, Rational Functions

7/27/2019 syllabus_OM013

2/2

Exponential and Logarithmic FunctionsExponential Functions, Logarithmic Functions, Evaluating Logarithms, Mathematical Model ing with Exponential

and Logarithmic Functions

Trigonometric FunctionsDefinitions of Trigonometric Functions, Values of Trigonometric Functions, Graphs of the Sine and Cosine

Functions, Graphs of Other Trigonometric, Functions, Inverse Trigonometric Functions

Trigonometric IdentitiesFundamental Trigonometric Identities, Sum and Difference Identities, Multiple, Angle Identities, Sum-to-

Product Identities, Evaluating Id entities, Trigonometric Equations

Applications of Trigono metryLaw of Sines, Law of Cosines, Vectors and Trigonometry, Trigonometric Form of Complex Numbers, DeMoivre's

Theorem

Systems of Equations and InequalitiesSystems of Linear Equations, The Matrix Method for Solving Systems, Properties of Matrices, Matrix Inverses,

Determinants, Cramer's Rule, Non-linear Systems of Equations, Systems of Inequalities

Additional TopicsMathematical Induction, The Binomial Theorem, Arithmetic Series, Geometric Series

LearningObjectives

Upon completion of Honors Precalculus with Trigonometry, students will demonstrate proficiency in:

Applying techniques related to the ab ove topics to solve p roblems Understanding the nature of rigorous logical thinking Expressing mathematics clearly, in both written and oral communication Working creatively toward solutions to novel problems Understanding the qualitative differences between linear, polynomial, rational, logarithmic, exponential, and

trigonometric functions as well as their typical applications

SampleAssignment

1. Find all fourth roots of . Write your answers in (exact) rectangular form.2. Solve the equation . Leave answers in trigonometric form.3. One rope pulls a barge directly east with a force of 100 newtons. Another rope pulls the barge to the northeast

with a force of 200 newtons. Find the resultant force acting of the barge, to the nearest unit, and the angle

between the resultant and the first rope, to the nearest tenth.

4. A plane has an airspeed of 520 mph. The pilot wishes to fly on a bearing of 310. A wind of 37 mph is blowingfrom a bearing of 212. What direction should the pilot fly, and what will be her actual speed?