Precalculus Lesson

The Broken Ferris Wheel Rescue: Evaluating Trig Functions on the Unit Circle

Shared by A STEM Educator

11th GradeThin-SlicingCCSS.MATH.CONTENT.HSF.TF.A.1, CCSS.MATH.CONTENT.HSF.TF.A.250 min

Learning Objective

Students will be able to convert between radian and degree measures (CCSS.MATH.CONTENT.HSF.TF.A.1) and use the unit circle to evaluate sine, cosine, tangent, and reciprocal trig functions at special radian values (CCSS.MATH.CONTENT.HSF.TF.A.2).

Lesson Overview

Students progress from identifying radian positions on the unit circle to evaluating all six trig functions at special angles, using the Ferris wheel rescue context to ground coordinates in meaning. Tasks thin-slice from converting radians to degrees, locating reference angles, reading coordinates, and finally evaluating reciprocal trig functions at non-standard positions.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Random grouping cards or tool
Printed unit circle reference (for consolidation only)
Sticky notes for exit slip

Scaffolded Task Progression

1Task 1

The Ferris wheel has radius 1. A gondola starts at the rightmost point (3 o'clock position) and rotates counterclockwise. Match each radian measure to its degree equivalent and its position on the wheel:
a) π/6b) π/4c) π/3d) π/2 For each: (i) convert to degrees, (ii) name the clock position (e.g., '2 o'clock'), (iii) identify which quadrant. [ Interactive graph / diagram — available in the full lesson ]

2Task 2

The rescue team knows the gondola is at angle π/3 on the unit circle. They remember that at this angle, the point on the circle is (1/2, √3/2).
a) What is the x-coordinate of the gondola's position?b) What is the y-coordinate?c) Using the unit circle definition, what is cos(π/3)? What is sin(π/3)?d) The Ferris wheel has radius 1. How high above the center is the passenger? [ Interactive graph / diagram — available in the full lesson ]

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