Graphing Basic Trig Functions
Graphing Basic Trig Functions
This activity is designed specifically with teachers in mind. Its purpose is to be used as a classroom demonstration, developing the fundamental concept of Cartesian graphs of the six basic trigonometric functions. We can see these assigned lengths related to various line segments associated with the angle and the unit circle. We then see how to take the unit circle representation of the trigonometric function on the left and translate it to the Cartesian graph on the right. The activity is created in a way to show how the measurement from the triangle directly corresponds to the wave graph of a sine or cosine function.
The angle Ɵ can be adjusted from -2π to 4π by the slider/input box combination. We first see this angle on the unit circle representation (on the left) as a signed arclength, indicated in magenta. This translates to a signed horizontal distance (also represented in magenta) on the Cartesian graph representation on the right. These are the two consistent representations of the input for all six trigonometric functions.