The Animated Unit Circle is a simple tool which uses animation to help Pre-Calculus students to explore and understand Circle Trigonometry better and to visualize the meaning of the 'sine wave' which is so important in describing many different natural phenomena. The sine and cosine of an angle are defined as the lengths of the y (orange) and x (green) coordinates of a point rotating counterclockwise around a circle of radius one (Unit Circle) centered at the origin. When you click on the Graphs button you can watch the sine (orange) and cosine (green) graphs in a separate screen, where the mapping between the coordinates of a point on the unit circle and the distance travelled around it (yellow) can be watched through the animation.
By using the app and its features (like visualizing the angle of reference for any given angle), students might just 'see' the answers to some usual questions they might be required to answer while learning Trigonometry such as:
- Name another angle with the same sine as 210°.
- What is the largest value of the sine function? What is the smallest value?
- Does the sine of angle increase or decrease as the angle increases from 180° to 270°?
- Find all values of an angle between 0° and 360° such that it sine is equal to -0.8192
- What is the reference angle of 190°?