Module 2 builds on students' previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This is an introduction to finding the arc length and area of sectors of circles. Students should have the formulas for Circumference and Area of circles.

In this video segment you’ll discover how using concentric circles can help you determine how much paint is needed to cover the deck of a carousel.

In this activity, students will investigate the construction of circles that pass through a given number of points. They will also investigate the number of points needed to generate a unique circle in a plane.

Given this lesson and either the diameter or radius of a circle, you'll be able to calculate the other measure.

Using circumference, this segment measures the total distant traveled by two carousel riders after the carousel has rotated 10 times.

The purpose of this task is to strengthen students' understanding of area. It could be assigned in class to individuals or small groups or given as a homework exercise to generate interesting discussions the following day. The relatively high levels of complexity and technical demand enhance its instructional value.

Sal determines if shapes are divided into 2 or 4 equal sections.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This discussion examines how to complete the square in circle equations. Students learn about the math concept through definitions and examples with detailed solutions.

Provides advanced information about circles through the use of examples and a brief video lesson. [1:00]

A definition, examples, and a video lesson all help to explain basic information about circles. [0:36]

This site teaches the Geometry of Circles to High Schoolers through a series of 1084 questions and interactive activities aligned to 9 Common Core mathematics skills.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Explains the basic concept of chords with step-by-step instructions and methods for solving specific problems on your own relating to this topic.

Explains the basic concept of circles with step-by-step instructions and methods for solving specific problems on your own relating to this topic.

This geometry lesson shows that that an inscribed angle is half of a central angle that subtends the same arc. [Geometry playlist: Lesson 24 of 31]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Inscribed angles and polygons are investigated through examples and a video lesson. [0:42]

CK-12's Texas Instruments Geometry Student Edition Flexbook is a useful collection of exercises intended to enrich a student's understanding of basic geometric principles.

In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles.  The module begins with the definition of dilation, properties of dilations, and compositions of dilations.  One overarching goal of this module is to replace the common idea of “same shape, different sizes” with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This task shows how to inscribe a circle in a triangle using angle bisectors. A companion task, ``Inscribing a circle in a triangle II'' stresses the auxiliary remarkable fact that comes out of this task, namely that the three angle bisectors of triangle ABC all meet in the point O.

This task is primarily for instructive purposes but can be used for assessment as well. Parts (a) and (b) are good applications of geometric constructions using a compass and could be used for assessment purposes but the process is a bit long since there are six triangles which need to be constructed.