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Summit Pre-Calculus/Trigonometry, Part 2 (MTH403B)

Summit Pre-Calculus/Trigonometry, Part 2 (MTH403B)

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Quick Overview

Pre-calculus weaves together concepts of algebra and geometry into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. Topics include quadratic, exponential, logarithmic, radical, polynomial, and rational functions; matrices; and conic sections in the first semester. The second semester covers an introduction to infinite series, trigonometric ratios, functions, and equations; inverse trigonometric functions; applications of trigonometry, including vectors; polar equations and polar form of complex numbers; arithmetic of complex numbers; and parametric equations.

Connections are made throughout the course to calculus and a variety of other fields related to mathematics. Purposeful concentration is placed on how the concepts covered relate to each other. Demonstrating the connection between the algebra and the geometry of concepts highlights the interwoven nature of the study of mathematics.

 

Teacher-Led Course (one-time payment)   $450.00

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Course Description

Pre-calculus weaves together concepts of algebra and geometry into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. Topics include quadratic, exponential, logarithmic, radical, polynomial, and rational functions; matrices; and conic sections in the first semester. The second semester covers an introduction to infinite series, trigonometric ratios, functions, and equations; inverse trigonometric functions; applications of trigonometry, including vectors; polar equations and polar form of complex numbers; arithmetic of complex numbers; and parametric equations.

Connections are made throughout the course to calculus and a variety of other fields related to mathematics. Purposeful concentration is placed on how the concepts covered relate to each other. Demonstrating the connection between the algebra and the geometry of concepts highlights the interwoven nature of the study of mathematics.

 

Prerequisite: MTH203: Geometry and MTH303: Algebra II (or equivalents)

Course Outline

SEMESTER 2

Unit 1: Introduction to Trigonometry: Linear Relationships

  • Introduction to Trigonometry
  • Introduction to Trigonometry: Linear Relationships and Functions
  • Relations, Functions, and Graphs
  • Slope, Linear Relations, Scatter Plots, and Piecewise Functions
  • Introduction to Trigonometry: Linear Relationships and Functions Unit Review

Unit 2: Trigonometric Ratios

Students begin a three unit exploration into trigonometry. In this unit, students review their understanding of the three basic trigonometric functions learned in geometry; sine, cosine and tangent; and extend this to include their reciprocal functions. Students learn radian measure and are introduced to the unit circle, the foundation of all of trigonometry.

  • Trigonometric Ratios
  • Angles and Angle Measures
  • Right Triangles and Trigonometric Ratios
  • The Unit Circle
  • Trigonometric Ratios Unit Review

Unit 3: Graph Trigonometric Functions

Students learn the graphs of the parent functions of the six trigonometric functions, as an extension of the unit circle, and explore transformations of these graphs. Students learn about inverse trigonometric functions and restrictions placed on them. Through applications of real-world problems involving trigonometric functions, students form connections between the algebra, the graph, and the description of scenarios that can be modeled with trigonometric functions.

  • Graphing Trigonometric Functions: Introduction
  • Graphing Trigonometric Functions
  • Transformations of Trigonometric Functions
  • Real-world Applications of Trigonometric Functions
  • Vectors
  • Graphing Trigonometric Functions Unit Review

Unit 4: Trigonometric Laws and Identities

The study of trigonometry provides an opportunity to investigate the algebra of trigonometry. This extends to the verification of trigonometric identities, applications of sum, difference, double, and half angle formulas, derivations and applications of the laws of sine and cosine, alternate methods of determining the area of a triangle, and an exploration into angular and linear velocities and how they are related to one another.

  • Trigonometric Laws and Identities
  • Law of Sines and Law of Cosines
  • Trigonometric Identities and Equations
  • Area of Triangles
  • Angular and Linear Velocities
  • Trigonometric Laws and Identities Unit Review

 

Additional Information

Course Length 4 Months
Prerequisites N/A
Course Materials

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Course Start Date

Courses Taught by a K12 Teacher

Courses with a teacher have designated start dates throughout Fall, Spring, and Summer. Full-year courses last 10 months and semester courses last 4 months. Courses are taught by teachers in K12 International Academy. For details on start dates, click here.

Teacher Assisted Yes, this course is taught by a K12 International Academy teacher. If you are looking for a teacher-supported option with additional flexibility and year-round start dates, click here to learn about the Keystone School, another K12 online private schooling option.
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To use this course, you'll need a computer with an Internet connection.  Some courses require additional free software programs, which you can download from the Internet.

Hardware and Browsers (Minimum Recommendations)

Windows OS

  • CPU: 1.8 GHz or faster processor (or equivalent)

  • RAM: 1GB of RAM

  • Browser: Microsoft Internet Explorer 9.0 or higher, Mozilla Firefox 10.0 versions or higher, Chrome 17.0 or higher

  • At this time our users are encouraged not to upgrade to Windows 10 or Edge (the new browser)

 

Mac OS

  • CPU: PowerPC G4 1 GHz or faster processor; Intel Core Duo 1.83 GHz or faster processor

  • RAM: 1GB of RAM

  • Browser: Firefox 10.0 versions or higher, Chrome 17.0 or higher (Safari is not supported!)

Internet Connections

It is highly recommended that a broadband connection be used instead of dial up.

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