Standard 2: Extend trigonometric functions to the unit circle.

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General Information
Number: MA.912.T.2
Title: Extend trigonometric functions to the unit circle.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Trigonometry

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Lesson Plans

Sine, Cosine, and Tangent: The Leap from Special Triangles to the Unit Circle:

Students will discover the connection between finding trigonometric ratios (sine, cosine, and tangent) using special right triangles and the unit circle.

Type: Lesson Plan

Round and Round the Unit Circle:

This lesson discusses the Unit Circle and how to use co-terminal and/or reference angles to find angles on the Unit Circle. It is an extension of trigonometric functions using the real number line.

Type: Lesson Plan

What is a Radian?:

Students participate in an activity that allows them to see physically and visually what a radian is. The lesson continues with the connection of radians and numbers expressed in terms of . Students will fill out a blank unit circle and provide themselves with their own "reference/study" guide for radian measures.

Type: Lesson Plan

Rotation Debate: Radians vs Degrees:

In this lesson, students will convert from degrees to radians and radians to degrees and calculate arc length using both degrees and radians. Students will come to consensus as to why radians are the preferred measure of an angle. This lesson normally takes two 50 minute class periods to teach.

  • Day 1: Bell Ringer-Day 1, Lesson Notes, Activity 1
  • Day 2: Day 1 Review and Wrap-up, Bell Ringer-Day 2, Activity 2

Type: Lesson Plan

Spinning Angles in Radians and Degrees (Introductory lesson to exact trigonometric values):

This lesson introduces concepts that are the prerequisites to defining trig functions on the unit circle. Radian measure and converting between degrees and radians are introduced. Students will also learn how to draw and measure positive and negative angles in standard position, identify and draw co-terminal angles, and determine a reference angle.

Type: Lesson Plan

Exact Trigonometric Ratios: Triangles to the Unit Circle:

This is a lesson in which the student learns and practices exact trig values. They are explained using triangles, then the unit circle, and then guided practice to be sure these concepts are mastered since they will be used in future problems in Pre-calculus and Calculus.

Type: Lesson Plan

Original Student Tutorial

Ferris Wheel Measures:

Learn about the radian measures of an angle, finding an angle measure in radians given the arc length and length of the radius, and converting between degree measures and radian measures in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

As the Wheel Turns:

In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context.

Type: Problem-Solving Task

Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorial

Ferris Wheel Measures:

Learn about the radian measures of an angle, finding an angle measure in radians given the arc length and length of the radius, and converting between degree measures and radian measures in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

As the Wheel Turns:

In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Problem-Solving Task

As the Wheel Turns:

In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context.

Type: Problem-Solving Task