Applets | |
|---|---|
| Polar to Rectangular Coordinate Conversion | This applet shows students how to convert rectangular to polar coordinates in a visual manner. It allows the user to pick various internal angles. |
| Interactive Unit Circle With Quadrants | This applet allows students to change the angle on an triangle that is inside a circle. The corresponding sin or cos waves are shown. Coordinates and quadrants can also be shown. |
| Interactive Unit Circle with Sine Chart | This applet shows the x,y coordinate, angle, sin, cos, tangent in degrees or radians, and shows the special angles. |
| Interactive Unit Circle to Sine and Cosine Graph | This applet shows the animation of the angles on unit circle creating the position for the sin and cos angle on the corresponding graph. Make sure to click the Sine and Cosine Animation button in the bar on the left screen. |
| Creation of the Ratios of Angles in Special Right Triangles | This applet helps the student discover how special right triangles are created and the relationships of their angles to corresponding sides. |
Resources |
|
| Unit Circle Game | This is a video game that allows multiple people to compete at filling out the unit circle values based on the prompts they receive. It's pretty fun! |
| Unit Circle Hit the Octopus Game | This is a fun video game that requires you to fill in the correct answer for the angles on the unit circle to launch a pie at an octopus! Let's hope you don't miss! |
| Unit Circle Quiz and Applet about 30 60 90 Triangle Properties | This is a resource that allows you to see how the angles relate to the sides of special triangles. There is an applet that allows you to visually see this. There are also practice problems with solutions to make sure you really understand the concept. |
| Unit Circle Construction Video | This is a great video by Kahn Academy that helps students understand how the unit circle is used to define sine, cosine, and tangent for all real numbers. |
| Unit Circle Solving for Triangles Video | This is a great video by Kahn Academy that helps students understand how to solve the triangles inside the unit circles. |
| Trigonometry Textbook | This is an amazing resource on trigonometry written by Ted Sundstrom and Steven Schlicker. This textbook lays the foundation for the discovery of certain relationships and the creation of the unit circle. This will help give students a deeper understanding about why the unit circle works the way it does and how it can help us in the real world. |
Cruzan, D. J. (n.d.). Angles: Degrees and Radians. Angle measurement. Retrieved October 17, 2021, from https://xaktly.com/AngleMeasurement.html
O'Conner, J. J., & Robertson, E. F. (n.d.). Trigonometric functions. Maths History. Retrieved October 17, 2021, from https://mathshistory.st-andrews.ac.uk/HistTopics/Trigonometric_functions/.
Angle. Learn and Practice Math - Math.net. (n.d.). Retrieved October 17, 2021, from https://www.math.net/angle
Radians. Math is Fun. (n.d.). Retrieved October 17, 2021, from https://www.mathsisfun.com/geometry/radians.html
Kendal, M., & Stacey, K. (1996, June). Trigonometry: Comparing ratio and unit circle methods.
In Technology in Mathematics Education. Proceedings of the 19th Annual Conference of the Mathematics education Research group of Australasia (pp. 322-329).
Hornsby, J., Lial, M. L., & Rockswold, G. K. (2011). A graphical approach to precalculus with limits: A unit circle approach. Addison-Wesley.
Dedsarte, P., & Genin, Y. (1990). On the role of orthogonal polynomials on the unit circle in digital signal processing applications. In Orthogonal polynomials (pp. 115-133). Springer, Dordrecht.
Hanbury, A. G., & Serra, J. (2001). Morphological operators on the unit circle. IEEE transactions on image processing, 10(12), 1842-1850.
Stapel, E. (n.d.). The Unit Circle. Purplemath. Retrieved October 19, 2021, from https://www.purplemath.com/modules/unitcirc.htm
Sources for Pictures:
Astrolabe Picture: https://electronics.howstuffworks.com/gadgets/clocks-watches/astrolabe.htm
Compass Pictures and Conversion Table from Degrees to Circle Fractions Picture: https://xaktly.com/AngleMeasurement.html
Initial and Terminal Side and Different Angle Types Pictures: https://www.math.net/angle
Transition Between Radian and Radius Picture: https://simple.wikipedia.org/wiki/Radian
Table for Conversion from Degree to Radians: https://www.cuemath.com/geometry/radians-to-degrees/
CAST Rule in a Unit Circle Picture: https://intomath.org/solving-trigonometric-equations/
SOHCAHTOA Picture: https://educationisaround.com/sohcahtoa/
Triangle Types Picture: https://mathbitsnotebook.com/Geometry/RightTriangles/RT306090.html
Combined Sine Function and Unit Circle Picture https://en.wikipedia.org/wiki/Unit_circle
Clock Picture https://www.zazzle.com/unit_circle_clock_blue_square_wall_clock-256859266608326321
Pictures of Reflections for the Unit Circle https://www.slideshare.net/kristinmiller929/unit-circle-48189733
Picture of Electrician https://www.istockphoto.com/photos/electrician
Polar Coordinates Picture https://keisan.casio.com/exec/system/1223527679
Resonance Picture http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/funhar.html