This lesson is an opportunity for students to use the unit circle to determine coordinates on circles of different sizes and circles whose centers are not at \((0, 0)\). Students find the coordinates of points on these circles and consider what they represent in context. They also consider the difference between approximating the coordinates and representing them exactly as expressions using cosine and sine. These ideas are developed further throughout the unit, leading eventually to the notions of amplitude and midline of trigonometric functions.
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems (MP5) and we recommend making technology available.
Lesson overview
 7.1 Warmup: Notice and Wonder: Big and Small (5 minutes)

7.2 Activity: Clock Coordinates (15 minutes)
 Includes "Are you Ready for More?" extension problem
 7.3 Activity: Around a Ferris Wheel (15 minutes)
 Lesson Synthesis
 7.4 Cooldown: An Airplane Propeller (5 minutes)
Learning goals:
 Use sine and cosine to evaluate/estimate coordinates of points on a circle in all 4 quadrants
Learning goals (student facing):
 Let’s find coordinates on a circle.
Learning targets (student facing):
 I can use cosine and sine to figure out information about points rotating in circles.
Required materials:
 Scientific calculators
 blackline master (optional)
Required preparation:
 It will be helpful for students to have access to scientific calculators if they choose to compute approximate trigonometric values to help give meaning to their answers in context.
 It may be helpful for some students to have extra copies of the gridded clock faces in the activity Clock Coordinates. Consider printing and making extras available using the Blackline Master.
 Devices are required for the digital version of the activity “Around a Ferris Wheel.”
Standards:
 This lesson builds on the standard: CCSS.HSFTF.AMS.FTF
 This lesson builds towards the standards: CCSS.HSFTF.BMS.FTFCCSS.HSFTF.B.5MS.FTF.5
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