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Standard 2 : Extend trigonometric functions to the unit circle.
Cluster Standards
This cluster includes the following benchmarks.
Visit the specific benchmark webpage to find related instructional resources.
- MA.912.T.2.1 : Given any positive or negative angle measure in degrees or radians, identify its corresponding angle measure between 0° and 360° or between 0 and 2π. Convert between degrees and radians.
- MA.912.T.2.2 : Define the six basic trigonometric functions for all real numbers by identifying corresponding angle measures and using right triangles drawn in the unit circle.
- MA.912.T.2.3 : Determine the values of the six basic trigonometric functions for 0,
, 
and 
and their multiples using special triangles. - MA.912.T.2.4 :
Use the unit circle to express the values of sine, cosine and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any real number.
- MA.912.T.2.5 : Given angles measured in radians or degrees, calculate the values of the six basic trigonometric functions using the unit circle, trigonometric identities or technology.
Cluster 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
Cluster Resources
Vetted resources educators can use to teach 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.
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.
- 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.
- 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. - 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
- 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.
- 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.
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.