Unit Plan
Oswego City School District

Regents Exam Prep Center: Unit Circle

For Students 9th - 10th Standards
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....
Lesson Plan
Texas Instruments

Texas Instruments: Chords, Secants, and Tangents

For Teachers 9th - 10th Standards
Young scholars construct chords, secants, and tangents. From those constructions, they develop a deeper understanding of the terms, as well as explore certain properties of the constructions.
Handout
Math Open Reference

Math Open Reference: Tangent

For Students 9th - 10th Standards
Learn about tangents with this handy reference guide. Provides detailed definitions, examples, and an interactive activity that enhances further explanation. Includes links to related topics.
Activity
Math Open Reference

Math Open Reference: Circles

For Students 9th - 10th Standards
A complete reference guide to circles including parts, angles, and arcs. It provides definitions and interactive activities that enhance further explanation.
Handout
Purple Math

Purplemath: The Unit Circle

For Students 9th - 10th Standards
Relates the unit circle to the method for finding trig ratios in any of the four quadrants. Demonstrates how the unit circle might be useful.
Handout
Math Open Reference

Math Open Reference: Parts of a Circle

For Students 9th - 10th Standards
Learn about parts of a circle with this pictorial index. Click on the diagrams for more information. Includes links to related topics.
Unit Plan
CK-12 Foundation

Ck 12: Exact Values for Inverse Sine, Cosine, and Tangent

For Students 10th - 12th Standards
[Free Registration/Login may be required to access all resource tools.] Find all angles on the unit circle matching exact trig ratios. Resource includes examples, videos, and practice problems.
PPT
Sophia Learning

Sophia: Two Lines Tangent to a Circle: Lesson 3

For Students 9th - 10th
This lesson will present how if two segments from the same point outside a circle are tangent to a circle, then they are congruent. It is 3 of 5 in the series titled "Two Lines Tangent to a Circle."
Lesson Plan
Illustrative Mathematics

Illustrative Mathematics: G C Mutually Tangent Circles

For Teachers 9th - 10th Standards
Three circles are mutually tangent. Students are asked to find the total area of the circles plus the area inside where they meet. Students will need to know how to calculate the area of a circle, a sector of a circle, and an equilateral...
Activity
Texas Instruments

Texas Instruments: Angles Formed by Intersecting Chords, Secants, and Tangents

For Teachers 9th - 10th Standards
In this activity, students will investigate properties of angles and arcs formed when chords, secants, and tangents intersect and intercept arcs in a circle. They discover several important theorems concerning circles and arc sizes. They...
Activity
CK-12 Foundation

Ck 12: Tangent Lines

For Students 9th - 10th
[Free Registration/Login Required] Students can adjust the size of the circle to explore the tangent lines. Click learn more to watch a video and click challenge me to answer a practice question.
Lesson Plan
Illustrative Mathematics

Illustrative Mathematics: g.c Inscribing a Circle in a Triangle I

For Teachers 9th - 10th Standards
The goal of this task is to show how to draw a circle which is tangent to all three sides of a given triangle: that is, the circle touches each side of the triangle in a single point. Aligns with G-C.A.3.
Handout
University of Regina (Canada)

Univeristy of Regina: Math Central: Tangent Lines and Circle Equations

For Students 9th - 10th Standards
This site offers a problem and solution to finding all possible slopes for a line tangent to a circle given a particular equation of a circle. Could be an interesting challenge for students.
Activity
CK-12 Foundation

Ck 12: Segments From Secants and Tangents

For Students 9th - 10th
[Free Registration/Login Required] Students will adjust points to explore secants and tangents of circles. Click learn more to watch a video and click challenge me to answer a practice question.
Activity
Analyze Math

Analyze Math: Unit Circle and Trigonometric Functions

For Students 9th - 10th Standards
The free mathematics tutorial explores the unit circle and trigonometric functions. The tutorial consists of definitions and examples with solutions. The interactive applet allows students to investigate domain, range, and asymptotes of...
Interactive
University of Colorado

University of Colorado: Ph Et Interactive Simulations: Trig Tour

For Students 9th - 10th Standards
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.
Lesson Plan
Illustrative Mathematics

Illustrative Mathematics: G Srt Tangent Line to Two Circles

For Teachers 9th - 10th Standards
The purpose of this task is to use similar triangles and setting up a proportion in order to calculate a side length. Aligns with G-SRT.B.5.
Handout
Geometry Help

Geometry Help: Tangent Lines

For Students 9th - 10th Standards
Explains the basic concept of congruent triangles with step-by-step instructions and methods for solving specific problems on your own relating to this topic.
Whiteboard
ClassFlow

Class Flow: Circles Geometry

For Teachers 6th - 8th Standards
[Free Registration/Login Required] Students identify segments and lines related to circles and the properties of a tangent to a circle.
Lesson Plan
Illustrative Mathematics

Illustrative Mathematics: F Tf Special Triangles 1

For Teachers 9th - 10th Standards
Using known facts about the unit circle and isosceles triangles together with the Pythagorean Theorem, students can derive the sine and cosine of special angles. Aligns with HSF-TF.A.3.
Lesson Plan
Illustrative Mathematics

Illustrative Mathematics: F Tf Special Triangles 2

For Teachers 9th - 10th Standards
Using known facts about the unit circle and isosceles triangles together with the Pythagorean Theorem, young scholars can derive the sine and cosine of special angles. Aligns with HSF-TF.A.3.
Activity
Ministerio de Educacion, Cultura y Deporte (Spain)

Cnice: Relacion De Ejercicios Interactivos.

For Students 9th - 10th
In Spanish. Interactive activities online on various geometric and trigonometric concepts such as area, perimeter, secants, tangents, etc. A terrific resource for students. Site is organized acoording to shape. (triangle, quadrilaterals,...
Activity
University of Vienna (Austria)

The Graphs of Sin, Cos, and Tan Maths Online

For Students 9th - 10th
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...
Interactive
Calculator Soup

Calculator Soup: Trigonometric Functions Calculator

For Students 9th - 10th Standards
This online trigonometry calculator will calculate the sine, cosine, tangent, cotangent, secant and cosecant of angle values entered in degrees or radians. The trigonometric functions are also known as the circular functions.

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