In this article, the author presents a Desmos activity where students adjust the measures of angles in radians to reposition a laser and a mirror so the beam passes through three stationary targets. This Radian Lasers activity can be extended to simulate project-based learning (PBL), a pedagogical approach for applying concepts and skills from…

Historical accounts of trigonometry refer to the works of many Indian and Arab astronomers on the origin of the trigonometric functions as we know them now, in particular Abu al-Wafa (ca. 980 CE), who determined and named all known trigonometric functions from segments constructed on a regular circle and later on a unit circle (Moussa 2011;…

Smartphones used as tools provide opportunities for the teaching of the concepts of accuracy and precision and the mathematical concept of arctan. The accuracy and precision of a trigonometric experiment using entirely mechanical tools is compared to one using electronic tools, such as a smartphone clinometer application and a laser pointer. This…

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…

A growing body of literature has identified quantitative and covariational reasoning as critical for secondary and undergraduate student learning, particularly for topics that require students to make sense of relationships between quantities. The present study extends this body of literature by characterizing an undergraduate precalculus…

In this article, the author describes the development and implementation of a measurement-based group activity designed to support students in understanding the connection between angle magnitude and the shape of the sine function. She explains that the benefit of this activity is that it allows students to build their trigonometric knowledge…

The study of trigonometry suffers from a basic dichotomy that presents a serious obstacle to many students. On the one hand, there is triangle trigonometry, in which angles are commonly measured in degrees and trigonometric functions are defined as ratios of sides of a right-angled triangle. On the other hand, there is circle trigonometry, in…

Many studies argue that dynamic features of the artefact Cabri may function as instruments of semiotic mediation. Our study is situated in this perspective and aims to observe the impact of the use of the technological artefact Cabri in a teaching experiment that introduces the notion of a trigonometry function, through the articulation of the…

This textbook covers geometry and trigonometry and presents problems for student consideration. Contents include geometry, plane trigonometry, analytical trigonometry, spherical trigonometry, and mensuration. [This book was adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, plane and spherical trigonometry, and mensuration. [This book was translated by David Brewster. It was revised and adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, plane and spherical trigonometry, and mensuration. [This book was translated by David Brewster. It was revised and adapted by Charles Davies.]

This textbook discusses ratios and proportions; the circle and measurement of angles; proportions of figures--measurement of areas; regular polygons--measurement of the circle; planes and polyhedral angles; polyhedrons; the cylinder, cone, and sphere; spherical geometry; plane trigonometry; analytical trigonometry; spherical trigonometry; and…

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, analytical trigonometry, plane and spherical trigonometry, and mensuration. [This book was revised and adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, analytical trigonometry, plane and spherical trigonometry, and mensuration. [This book was revised and adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, analytical trigonometry, plane and spherical trigonometry, and mensuration. [This book was revised and adapted by Charles Davies.]