Interactive Desmos animation relating the graphs of sin(x) and cos(x) to the unit circle.
Type of Material:
Simulation
Recommended Uses:
The material would be well suited to use for in-class demonstrations or individual exploration.
Technical Requirements:
Any Browser
Identify Major Learning Goals:
The main goal of this site is to aid users in visualizing the unit circle and the graphs of sin(x) and cos(x), and to show the periodic functions.
Target Student Population:
High School, College Lower Division
Prerequisite Knowledge or Skills:
Pre-Calculus, Algebra, Trigonometry
Content Quality
Rating:
Strengths:
This Desmos applet is interactive and user friendly. Users can display the unit circle, the coordinates of points on the unit circle, and can watch the graphs of sin(x) and cos(x) generated as a point is rotated about the unit circle. This visual demonstration will be quite beneficial to many trigonometry students. Users can choose which components to display by clicking on the circle to the left of each component. Users can also pause the animation and use the slider to choose an angle (in radians).
Concerns:
The problem that the rotation is fast, and you cannot change the speed. The user does not provide the formula to show the periodic equivalent values with the number of the revolutions.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This applet is a great tool for helping students to visualize points on the unit circle and how the unit circle is related to the graphs of sin(x) and cos(x). In addition, the learner could add the graphs of other functions. Since it is on Desmos, the coordinates of points can be displayed on the added graphs, and the grid can be added so you can see, for example, the range.
Concerns:
The site could be improved by including a brief overview of the unit circle and how it is related to material in trigonometry or, perhaps, a link to more information. In addition, formulas could be added.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This applet is interactive and intuitive. The use of different colors for different components of the graph is visually appealing.
Concerns:
The speed of animations cannot be adjusted.
Creative Commons:
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