Lesson 18

In this lesson students practice using trigonometric functions to model the circular motion of a rider on a carousel. The motion of the riders relative to the center of the carousel has a midline of 0, but the amplitude, period, and horizontal translation all need to be interpreted from the context.

Students use the structure of the unit circle to explain why the graphs of the functions defined by \(y=\sin\left(\frac{\pi}{2} + x\right)\) and \(y= \cos(x)\) are actually the same (MP7), noting that a rotation of \(\frac{\pi}{2}\) in the counterclockwise direction takes the horizontal coordinate of a point on the unit circle to the vertical coordinate of the image point on the unit circle. 

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.