Introduction to Sine and Cosine

Abstract

This activity is designed to build intuition of the definition of radian measure of an angle and to build toward finding the values of 16 special angles on the Unit Circle. It emphasizes the points which are on the coordinate axes (i.e., points which are multiples of π/2). Other points are introduced to foreshadow future lessons, but it is not expected that students possess the knowledge to find cos(3π/4) at this point. A connection is made between the geometry of a circle and the function framework for the definition of sine and cosine. The functions sin and cos are defined in this lesson. The Extension Questions get students thinking about negative angles and angles larger than 2π.

Level: High School or Undergraduate
Setting: Classroom
Activity Type: Learning Cycle
Discipline: Mathematics
Course: Trigonometry
Keywords: Unit Circle, Pythagorean Theorem, sine, cosine, angles