Learning Resources
Overview
Mathematical Modeling, Book 2 focused a great deal on trigonometry. This unit of study will extend on that knowledge, as trigonometry is explored and applied in various contexts. By extending your knowledge of radian measure to a study of odd and even functions, combinations of trigonometric functions, rotational matrices, and trigonometric identities, you should have a thorough understanding of trigonometry upon which to enter your postsecondary studies.
This unit of study contains five sections as outlined below.
Section 4.1: reviews radian measure and its applications. You will investigate the connection between radian measure and arc length, and use this knowledge to solve related problems. Connections between the sine and cosine functions will also be revisited and their symmetry properties will be analyzed as a means of examining equivalent trigonometric relations. The familiar Ferris wheel problem appears again as a means by which to introduce you to the tangent function as a combination of the sine and cosine functions. By the end of this section , you will have a good understanding of the graphs of all three primary trigonometric functions.
Section 4.2: reviews the graphing of trigonometric functions written in transformational form. The patterns involved in graphing sine and cosine functions are extended to graph the tangent function and the reciprocal trigonometric functions in transformational form.
Section 4.3: deals with matrices and the general rotational matrix. A brief review of the multiplication of matrices will be provided, leading to the investigation and development of the rotational matrix from your understanding of the unit circle and the unit vectors.
Section 4.4: involves working with trigonometric identities, solving trigonometric equations and inverse trigonometric functions. You will use the skills gained form your study of trigonometric equations and graphs in Mathematical Modeling, Book 2 to verify or reject various trigonometric identities.
Section 4.5: extends your understanding of combinations of functions from Chapter 2 to trigonometric functions. You will explore patterns and predict the shape of the graph of any function or function combination.
This unit of work should take approximately 20 hours to complete.
The following supplies are needed for the completion of this unit of study.
- compass
- protractor
- graph paper
- straws
- ruler
- cardboard
- pushpins or thumbtacks
- 3 coloured pencils
To complete the chapter project, you will need the following supplies.
- multi-link cubes
- flour sugar
- water
- gelatin