CK-12 Foundation
Ck 12: Trigonometry: Trigonometric Functions and Angles of Rotation
[Free Registration/Login may be required to access all resource tools.] Describing trig functions as relationships on the unit circle.
Mathigon
Mathigon: Geometry: Circle and Pi: Degrees and Radians
Rather than dividing a circle into some number of segments (like 360 degrees), mathematicians often prefer to measure angles using the circumference of a unit circle - a circle with radius 1. This way of measuring angles is called...
Lawrence Hall of Science
The Math Page: Trigonometry: Analytic Trigonometry the Unit Circle
Here is a site that clearly and thoroughly explains the unit circle and all six trigonometric functions of all quadrantal angles. There are example problems solved, problems for the student to attempt, and answers to the student...
Texas Instruments
Texas Instruments: Exploring the Unit Circle
In this activity, students explore the properties of a unit circle and its mapping functions.
Oswego City School District
Regents Exam Prep Center: Unit Circle
Two hands-on lab activities for instructors to use when teaching about the coordinate graphs of the sine, cosine, and tangent functions derived from a unit circle. The graphs of the reciprocals of the three functions are investigated....
Illustrative Mathematics
Illustrative Mathematics: F Tf Properties of Trigonometric Functions
The goal of this task is to use the unit circle and rigid transformations in order to establish some fundamental trigonometric function identities. Aligns with F-TF.A.2 and F-TF.A.4.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Graph of Circle as a Function
Dr. Math, in a reply to a student question, describes how a circle can be a function.
Paul Dawkins
Paul's Online Notes: Algebra: Graphing and Functions
Students investigate functions and graphing. Topics examined are lines, circles, graphing functions, inverse functions, and combining functions. Class notes, definitions, and examples with detailed solutions are included. The class notes...
Illustrative Mathematics
Illustrative Mathematics: F Tf Trig Functions and the Unit Circle
The purpose of this task is to help students make the connection between the graphs of sin t and cos t and the x and y coordinates of points moving around the unit circle. Students have to match coordinates of points on the graph with...
Illustrative Mathematics
Illustrative Mathematics: G Gpe.5 Triangles Inscribed in Circle
In this task, students use ideas about linear functions to determine when certain angles are right angles. They use the fact that two lines (if not vertical or horizontal) are perpendicular when their slopes are inverse reciprocals, as...
Analyze Math
Analyze Math: Applications and Use of the Inverse Functions
Learners explore applications of inverse functions. Topics investigated are angle of elevation, range, and right circular cones. The activity includes examples on uses of inverse functions in real situations with detailed solutions.
Alabama Learning Exchange
Alex: Traveling Around the Unit Circle
This lesson is intended to review the key ideas associated with trigonometric functions.The design of this lesson provides a collection of reproducible activities to be used in a classroom setting where students have varied backgrounds /...
Texas Instruments
Texas Instruments: Trig Values of the Unit Circle
This is a LearningCheck quiz to evaluate students on the special angles of the unit circle.
Wolfram Research
Wolfram Math World: Hyperbolic Functions
This site from MathWorld explains the hyperbolic function. The information is not too in-depth, but factual and quite a few links are provided for additional information on related subjects.
Analyze Math
Analyze Math: Special Angles on Unit Circle
Learners explore the special angles between 0 and 2 pi on a unit circle. The special angles can be used to solve trigonometry problems.
Clark University
Clark University: Dave's Short Trig Course: Trigonometric Functions
The Clark University site shows and explains the graphs of the six trigonometric functions. It explains how to find an arbitrary angle measurement using trig. Also, it explains that sine and cosine functions are complementary.
Purple Math
Purplemath: Trigonometric Functions and Their Graphs
Explains the horizontal forms of trigonometric graphs by showing how they relate to the circular graphs.
Illustrative Mathematics
Illustrative Mathematics: F Tf Trigonometric Functions for Arbitrary Angles
The purpose of this task is to examine trigonometric functions for obtuse angles. Aligns with F-TF.A.2.
Texas Instruments
Texas Instruments: "The Sound of Music"
This activity will use tuning forks and the CBR to gather sound wave data for students to use to write Sine (or Cosine) functions. In this activity we study waves of known musical notes before studying waves of unknown musical notes. I...
Student Achievement Partners
Student Achievement Partners: Penny Circle Task [Pdf]
Learners will explpre models and understand the difference between quadratic, exponential, and linear models in this lesson.
Illustrative Mathematics
Illustrative Mathematics: G Srt, G Mg Seven Circles Iii
In this task, students are shown circle formations where an inner circle is surrounded by a set of circles and all circles are touching. In the first situation, all circles have the same diameter. In the second, the inner circle is...
Northeast Parallel Architectures Center, Syracuse University
Npac Reu Program: Trigonometric Functions
This Northeast Parallel Architectures Center of Syracuse University site offers a quick overview of the six trigonometric functions from the standpoint of the unit circle.
University of Maryland
University of Maryland: Romantic Circles
Extensive site dedicated to Romantic Studies. Best to use the search function. Includes modern poets reading Romantic poetry.
McGraw Hill
Glencoe Mathematics: Quiz on Trigonometric Functions on the Unit Circle
Learners demonstrate comprehension of advanced mathematical concepts in Trigonometry. The questions check understanding on the topic of trigonometric functions on the unit circle.