Lesson 7: Using the Unit Circle to Define Trigonometric Functions
Standard Addressed
MCC9-12.F.TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
Brief Lesson Overview
In this lessons students will "unwrap" the Unit Circle. Students should work in pairs or small groups (no more than 4). This is an exploratory lesson with minimal direct instruction. The teacher acts a facilitator and resource for the students but does not lecture.
The activity allows students to use the concepts they learned about the Unit Circle to define the graphs of sine and cosine. You can either let groups graph both functions or assign some groups the sine function and others the cosine function. If you decide to divide the graphs between groups, you may want to edit the attached dacoument because it was created for students to do both graphs. Read through the activity prior to assigning it to your students.
This activity can be used as a culminating activity or a formative assessment and it launches intp the Unit on Graphs of Trigonometric Functions. Make sure you have enough room for students to spread out. Also, the fettuccine noodles are sturdier and less likely to break and/or roll away during the actvity.
Materials needed:
The activity allows students to use the concepts they learned about the Unit Circle to define the graphs of sine and cosine. You can either let groups graph both functions or assign some groups the sine function and others the cosine function. If you decide to divide the graphs between groups, you may want to edit the attached dacoument because it was created for students to do both graphs. Read through the activity prior to assigning it to your students.
This activity can be used as a culminating activity or a formative assessment and it launches intp the Unit on Graphs of Trigonometric Functions. Make sure you have enough room for students to spread out. Also, the fettuccine noodles are sturdier and less likely to break and/or roll away during the actvity.
Materials needed:
- Bulletin Board paper or Butcher paper (about 8 ft.)
- Spaghetti or fettuccine noodles (uncooked)
- Masking Tape
- Yarn (about 7 feet long)
- Compass (optional)
- Protractor
- Markers
- Rulers and Yard Sticks
- Unit circle (angle and coordinate values)
After students have completed the "Unwrapping the Unit Circle" Activity you can use this applet to demonstrate this process dynamicaly. If students have a QR reader they can scan the QR code at the top of the page.