Texas Instruments
Texas Instruments: Circular Functions
In this activity, students find intercepts of circular function graphs. They also investigate the characteristics of such graphs.
Better Lesson
Better Lesson: Algebra Ii: The Trigonometric Functions
A lesson plan where students will interpret the trigonometric functions in terms of the unit circle, graph a sinusoidal function, and use a sinusoidal function to make interpretations in a modeling context.
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.
Cuemath
Cuemath: Cosecant, Secant and Cotangent Functions
Features graphs of the trigonometric functions cosecant, secant, and cotangent. Includes solved examples and practice questions.
University of Vienna (Austria)
The Graphs of Sin, Cos, and Tan Maths Online
This applet allows the user to create the graphs of sin, cos, and tan by moving a scroll bar. The user can watch the unit circle and the graph simultaneously to see how the two are related. The user may also choose to see the angle...
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....
Purple Math
Purplemath: Trigonometric Functions and Their Graphs
Explains the horizontal forms of trigonometric graphs by showing how they relate to the circular graphs.
CK-12 Foundation
Ck 12: Trigonometry: Tangent and Cotangent Graphs
[Free Registration/Login may be required to access all resource tools.] Define the tangent and cotangent graphs using the unit circle.
CK-12 Foundation
Ck 12: Algebra Ii: 4.2 Right Triangle Trig Extended to Circles With a Model
This section explores the relationship between right triangles, circles, and trigonometry. It investigates how a right triangle that is set inside a circle and rotates around the circle is connected to trigonometric functions and their...
CK-12 Foundation
Ck 12: Trigonometry: Cosine and Secant Graphs
[Free Registration/Login may be required to access all resource tools.] Define the cosine and secant graphs using a unit circle.
CK-12 Foundation
Ck 12: Algebra Ii: 4.5 Graphing Sine and Cosine
This section explores the graphs of sine and cosine functions. It investigates how these graphs are related to coordinates for different angles in a unit circle.
Math2
Math2.org: Algebraic and Conic Section Graphs
THis resource provides examples and information about Algebraic graphing.
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...
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.
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...
Paul Dawkins
Paul's Online Notes: Algebra: Common Graphs
Students investigate how to graph a wide variety of equations and functions. Topics explored are lines, rational functions, parabolas, ellipses, and transformations. Class notes, definitions, and examples with detailed solutions are...
University of Colorado
University of Colorado: Ph Et Interactive Simulations: Trig Tour
Take a tour of trigonometry using degrees or radians! Look for patterns in the values and on the graph when you change the value of theta. Compare the graphs of sine, cosine, and tangent.
Illustrative Mathematics
Illustrative Mathematics: F Tf, G Co, Trigonometric Identities and Rigid Motions
The purpose of this task is to apply translations and reflections to the graphs of the functions f(x)=cos x and g(x)=sin x in order to derive some trigonometric identities. There are also rotations 180 degrees about points on the x-axis...
Shodor Education Foundation
Shodor Interactivate: Conic Flyer
"This applet allows the user to create graphs of conic sections. Using slider bars, one can manipulate the function to change the constant values and view the effects of those changes."
Curated OER
Trig Function Point Definitions
A java applet that relates the unit circle to the graphs of the six trigonometric functions, complete with the values of the functions.
Curated OER
Parametric Unit Circle
This site provides definitions for different parts of a circle, pictures to more clearly represent formulas involving circles. Some of the formulas discussed include: area of a circle, area of a sector of a cirles, circumference, length...
Math2
Math2.org: Trigonometry Tables
Three trig tables are provided for student and teacher reference. The first table lists the sine, cosine, tangent, secant, cosecant, and cotangent values of all whole-number angles from 0 to 90. The radian equivalent (to four decimals)...
Illustrative Mathematics
Illustrative Mathematics: F if Model Airplane Acrobatics
In this task, a model airplane pilot is practicing flying her airplane in a big loop for an upcoming competition. The task could serve as an introduction to periodic functions and as a lead-in to sinusoidal functions. By visualizing the...
Math2
Math2
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