# Trigonometry

## Introduction

This page contains resources that may be of interest to students studying Trigonometry. The number of resources on this page will grow as additional items are developed. If you have any questions or special requests, please contact Earl at mathguy.us@gmail.com.

## Chapter Notes

#### Teacher Notes for 2024-25 Trigonometry

- 2024 Chapter 4 Part 1 Notes - Introduction to Trigonometry and the Unit Circle

#### Previous Years Notes related to Trigonometry

- Chapter 4 Part 1 Notes - Mr H. Notes - Angles and Radian Measure, Arc Length, Right Angle Trigonometry, Unit Circle, Trig Functions of Any Angle
- Chapter 4 Part 2 Notes - Mr H. Notes - Graphs, Inverse Trig Functions, Applications, Simple Harmonic Motion
- Chapter 5 Notes - Mr H. Notes - Identities, Formulas, Equations
- Chapter 6 Notes - Mr H. Notes - Laws of Sines and Cosines, Area formulas, Vectors, Comples Numbers
- Chapter 6 Notes - Mrs A. Notes - Laws of Sines and Cosines, Area formulas, Vectors, Complex Numbers
- Plot a Polar Curve - Geogebra.com provides an online plotting program that allows the student to watch the plotting of a Polar Curve as the angle increases from 0 to 2
*π*radians. Enter the equation and drag the slider to watch the curve being plotted. - Print Polar Graph Paper - The graph paper app (for PCs) allows you to print graph paper for plotting polar or Cartesian curves. Download and install the program (open the zip file, then double-click on the "setup" file), run it, and select how you want your graph paper to look. There are lots of options for how you want your graph paper to look. Then, use the Windows snipping tool to cut and paste the graph paper into your application or onto a blank document for printing.

## Sample Tests, Reviews, Alternative Assignments, and Solutions

#### Problems related to Trigonometry

The value of reviewing these sample problems and solutions is twofold. The more obvious benefit relates to problems that a student has difficulty solving themselves; a solution is provided. Less obvious is the set of techniques used in our solutions; some of the techniques used on the sample problems may not be taught in the classroom. We concentrate on efficient solutions and shortcuts; so a review of the solved problems may present new techniques that enable a student to be more efficient in their approach to solving problems.

Sample Tests, Reviews, and Alternate Assignments (Blitzer Chapters 4 to 6) - Current

- DRHS Math Trigonometry Page
- Graph paper - Catesian and Polar - Design and print your own with easy point and click. Install the program on your PC, then have at it. Defaults may work well for you, or change them as desired. After you design the graph paper, use Windows' snipping tool to copy it into your own document.

- 2024 Chapter 4 Part 1 Review and Solutions - Trigonometric Functions and Their Values
- 2021 Chapter 4 Part 1 Review and Solutions - Trigonometric Functions and Their Values
- 2021-22 Chapter 4 Part 2 Sample Test and Solutions - Trigonometric Functions and Analytic Trigonometry

- 2024 Chapter 5 Alternative Assignments - Analytic Trigonometry (angle addition, double angle, half angle, Trigonometric equations)
- 2024 Chapter 5 Alternative Assignments - Solutions - Analytic Trigonometry (angle addition, double angle, half angle, Trigonometric equations)

- 2021-22 Chapter 5 Sample Test and Solutions - Analytic Trigonometry (angle addition, double angle, half angle, Trigonometric equations)
- 2021-22 Chapter 6 Sample Test and Solutions - Additional Topics (Laws of Sines and Cosines, Oblique Triangles, Polar Coordinates and Forms, Vectors)
- 2021-22 Semester 1 Review Problems and Solutions - Covers Semester 1 Precalculus and Trigonometry topics.
- Semester 1 Cumulative Test solutions will be posted on the Pre-Calculus page after the test is handed in.
- 2021-22 Semester 2 Review Problems and Solutions - Covers Semester 2 Precalculus and Trigonometry topics.

Additional Sample Tests and Reviews (Blitzer Chapters 4 to 6) - Previous Years

- 2021-22 Chapter 4 Part 1 Sample Test and Solutions - Trigonometric Functions and Analytic Trigonometry
- Older Chapters 4 and 5 Sample Test and Solutions - Trigonometric Functions and Analytic Trigonometry
- Older Chapters 4 Sample Test #2 and Solutions - Trigonometric Functions and Analytic Trigonometry. Note: there are two files here; solutions are hand-written
- Older Chapter 5 Sample Test #2 and Solutions - Analytic Trigonometry (angle addition, double angle, half angle, power reduction, product-to-sum, sum-to-product formulas)
- Older Chapter 6 Sample Test #2 and Solutions - Additional Topics (Laws of Sines and Cosines, Oblique Triangles, Polar Coordinates and Forms, Vectors)
- Semester Review - Hard Problems and Their Solutions - A list of probems that students found particularly difficult in preparing for the final

## Handbooks

Students of Trigonometry may find the following to be useful references.

- Algebra and PreCalculus Handbook version 3.5 – Covers two years of Algebra and one year of Pre-Calculus.
- Trigonometry Handbook version 2.4 – Covers High School Trigonometry. Special thanks to Butterfly Hall for discovering and developing the Butterfly Method for solving the Ambiguous Triangle (Chapter 6).

For more information on the handbooks, including download instructions, go to the Math Handbook page.

## PC Apps

The Trigonometry App has limited capabilities at this time, but may be of interest nonetheless.

- Trigonometry App version 0.7g – Covers topics in Trigonometry.

For more information on the PC Apps, including download instructions, go to the PC Apps page.

## TrigStar Sample Tests

The TrigStar Program Contest is an annual high school mathematics competition sponsored by the National Society of Professional Surveyors. You can visit their website here. National and local awards are provided for contest winners.

A formula sheet for use on the exams, as well as a number of practice tests, are provided below.

- Formula Sheet for use on TrigStar Tests

- 2002 Sample Test
- 2003 Sample Test
- 2004 Sample Test
- 2005 Sample Test
- 2006 Sample Test
- 2011 Sample Test and Step-by-Step Solutions
- 2012 Sample Test