How do students think about an angle measure of ninety degrees? How do they think about ratios and values on the unit circle? How might angle measure be used to connect right-triangle trigonometry and circular functions? And why might asking these questions be important when introducing trigonometric functions to students? When teaching…

This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the…

Discusses a method of graphing polar equations using information from the Cartesian graphs of trigonometric functions. (MKR)

Using MAPLE enables students to consider many examples which would be very tedious to work out by hand. This applies to graph plotting as well as to algebraic manipulation. The challenge is to use these observations to develop the students' understanding of mathematical concepts. In this note an interesting relationship arising from inverse…

Describes a five-step graphing method for various trigonometric periodic functions. Emphases is on teaching constants and functions. (YP)

Provides activities that introduce the sine and cosine functions in a hands-on manner. Includes ideas for assessment. Contains reproducible student worksheets. (MKR)

This is the second edition of a curriculum guide for secondary school mathematics. It is one of a series intended to serve as a model for Alaskan school districts as they develop and review their curriculum documents. Listed are topics and concepts, learning outcomes and objectives, and sample learning activities. The learning activities are…

A programing approach is described, using numerical methods to draw implicit functions, without solving the relationships explicitly. Several examples are discussed, with programs and printouts included. (MNS)

Describes an activity for making the connection between triangle ratios and graphs of circular functions which helps middle school students understand the concept of a sine curve. (ASK)

To help students develop measurement skills using metric units, an activity on making a box is described, with a worksheet for students. A second article discusses graphing elementary functions with a real domain, while a third article describes computer-assisted practice in graphing sine and cosine functions. (MNS)

This article, which is organized around a single, well-known algorithm for root extraction, presents a way of incorporating dynamical systems into the teaching of mathematics. Included are sample exercises using complex numbers and the computer where students have the opportunity to do some analysis on this algorithm. (KR)

Discussed is the place and teaching of trigonometry in a NCTM Standards-based mathematics curriculum. Presented is how these standards can be implemented in a technology-rich environment that encourages reasoning, communication, problem solving, and confidence building. Examples focus on functions, graphical sense, modeling, and identities. (KR)

Examples of composite functions present students with intriguing questions that they can explore using calculators and computers, geometric and algebraic methods, and approximation techniques. Student-centered activities allow students to make discoveries about functions. (MLN)

Presents three teaching ideas: (1) a scoring rubric to assess students' ability to communicate attempts at solving homework problems; (2) a three-part measurement activity using trigonometry, maps, and compasses to locate hidden treasure; and (3) a demonstration of the effects of numerical coefficients on graphs of quadratic functions. (MDH)