OML Search

Unit Circle (Symmetry, Periodicity)


Videos and lessons to help High School students learn how to use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Common Core: HSF-TF.A.4

Related Topics:
Common Core (Functions)

Common Core for Mathematics

Symmetry (Even and Odd)

Trigonometric Functions F.TF.4
Trigonometric Functions are developed and explored by changing one of the angles in a right triangle
Odd and Even Properties of Trig Functions F.TF.4
Odd and Even Symmetry of the Trigonometric Functions

Even and Odd Trig Functions
Review of Even and Odd functions, and introduction to the Even and Odd properties of Trigonometric Functions

Examples with Trigonometric Functions: Even, Odd or Neither.


Periodicity of Trigonometric Functions

Animation: Graphing the Sine Function Using The Unit Circle
This video is an animation of graphing the sine function using the unit circle.

Illustrating Sine with the Unit Circle
Move the slider or the locators to draw the graph of the sine function.

Animation: Graphing the Cosine Function Using the Unit Circle

Illustrating Cosine with the Unit Circle
Move the slider or the locators to draw the cosine function.

Animation: Graphing the Tangent Function Using the Unit Circle

Sine, Cosine, Tangent and the Unit Circle
Let x be an angle measured in radians drawn in standard position together with a unit circle. The radian measure of x is the length of the arc on the unit circle subtended by the angle. The sine of the angle is the y coordinate of the point where the terminal side of the angle intersects the unit circle, the cosine of the angle is the x coordinate of this same point, and the tangent of the angle is the slope of the line passing through the same point and the origin. the graphs of sine, cosine, and tangent are created directly from this unit circle interpretation of the three functions.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

[?] Subscribe To This Site

follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines