Radnor High School Course Syllabus

Trigonometry444

Credits: 1 Grades: 11-12Unweighted Prerequisite: Length: Year Algebra 2Format: Meets Daily or teacher recommendation

Overall Description of CourseTrigonometry is a College Preparatory level course.

College Preparatory level courses will feature moderate pacing and workload with teacher guidance to assist in the mastery of the material. Students enrolled on this level should be seeking to satisfy college requirements/expectations of mathematics courses but not necessarily have an interest in pursuing math related college majors.

The goal of this course is to examine trigonometric concepts and application and explore appropriate discrete topics. Trigonometry will be taught using both a right triangle and unit circle approach. Probability, statistics, exponential and logarithmic functions, sequences and series, and as time allows, other topics in discrete math will be introduced. Many of them have applications in engineering, management, and the social sciences.

MARKING PERIOD 1 – TOPICS

Review of Essential Algebra Skills

Distance & Midpoint Formulas Slope & Equations of Lines Function Notation, Domain & Range Factoring Solving Equations & Inequalities Addition & Subtraction of Rational Expressions Complex Fractions Equations w/Rational Expressions

Trigonometric Concepts

Angles Angle Relationships and Similar Triangles Definitions of the Trigonometric Functions

Modified 9/1/2011

Using the Definitions of the Trig Functions Trigonometric Functions of Acute Angles Trigonometric Functions of Non-Acute Angles Finding Function Values Using a Calculator Solving Right Triangles Further Applications of Right Triangles

MARKING PERIOD 2 – TOPICS

Trigonometric Concepts (cont.)

Radian Measure Applications of Radian Measure Circular Functions of Real Numbers Linear and Angular Velocity Graphs of the Sine and Cosine Functions Translations of Graphs Graphs of the Other Circular Functions Basic Trigonometric Identities & Proofs

MARKING PERIOD 3 – TOPICS Trigonometric Concepts (cont.)

Sum and Difference Identities for Cosine Sum and Difference Identities for Sine, Tangent Double-Angle Identities Half-Angle Identities Inverse Trigonometric Functions Trigonometric Equations I Trigonometric Equations II Equations Involving Inverse Trig Functions Oblique Triangles and the Law of Sines The Ambiguous Case of the Law of Sines The Law of Cosines

MARKING PERIOD 4 – TOPICS

Algebra & Discrete Topics

Exponential Functions Logarithmic Functions Evaluating Logarithms; Change of Base Exponential and Logarithmic Equations Complex Numbers Sequences and Series

Common Core Standards

Perform arithmetic operations with complex numbers.

N-CN.1. Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.

N-CN.2. Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

N-CN.3. (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Represent complex numbers and their operations on the complex plane.

N-CN.4. (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

N-CN.5. (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°.

N-CN.6. (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

Use complex numbers in polynomial identities and equations.

N-CN.7. Solve quadratic equations with real coefficients that have complex solutions.

Write expressions in equivalent forms to solve problems.

A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★

a. Factor a quadratic expression to reveal the zeros of the function it defines.

b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

A-SSE.4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.

Rewrite rational expressions.

A-APR.7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Understand solving equations as a process of reasoning and explain the reasoning.

A-REI.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-REI.2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Solve equations and inequalities in one variable.

A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients

Keystone Connections:

Student Objectives:

To develop the ability to think mathematically. To enhance problem solving ability. To utilize technology appropriately. To understand algebra as a study of the structure of the real and complex number

systems. To appreciate the usefulness of algebraic techniques. To continue to understand the concept of function as a unifying concept in

mathematics. To develop algebraic skills and concepts as a foundation for subsequent study of

mathematics. To reason and communicate mathematically. To represent situations which involve variable quantities with expressions, equations,

and inequalities. To challenge and expand the inquisitive and logical minds of the accelerated

mathematics students.

Materials & Texts Trigonometry Lial, et al – Addison Wesley – 7th edition

Graphing Calculator, preferably TI-84 Plus

Activities, Assignments, & AssessmentsACTIVITIESDiscovery Modules for various topics

ASSIGNMENTSAssignment sheets will be distributed periodically throughout the school year. Homework will be

assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics Department page of Radnor High School’s web site.

ASSESSMENTSGrades will be based on quizzes and tests. In addition, teachers may use homework, group activities, and/or projects for grading purposes. All students will take departmental midyear and final exams. The Radnor High School grading system and scale will be used to determine letter grades.

TerminologyNew terminology will be introduced at appropriate times within the development of the topics of the course. See topics list.

Media, Technology, Web ResourcesTI-8_ Graphing Calculator